线性代数示例

$[\begin{array}{c} - \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 1

将 $\frac{1}{\sqrt{2}}$ 乘以 $\frac{\sqrt{2}}{\sqrt{2}}$ 。

$[\begin{array}{c} - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2

合并和化简分母。

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解题步骤 2.1

将 $\frac{1}{\sqrt{2}}$ 乘以 $\frac{\sqrt{2}}{\sqrt{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2.2

对 $\sqrt{2}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2.3

对 $\sqrt{2}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2.6

将 ${\sqrt{2}}^{2}$ 重写为 $2$ 。

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解题步骤 2.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{2}$ 重写成 $2^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2.6.4

约去 $2$ 的公因数。

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解题步骤 2.6.4.1

约去公因数。

解题步骤 2.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 2.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 3

将分子乘以分母的倒数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{2}) & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 4

约去 $0.5$ 的公因数。

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解题步骤 4.1

从 $2$ 中分解出因数 $0.5$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{0.5 (4)}) & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 4.2

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{0.5 \cdot 4}) & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 4.3

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 5

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6

合并和化简分母。

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解题步骤 6.1

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6.2

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6.3

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6.6

将 ${\sqrt{3}}^{2}$ 重写为 $3$ 。

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解题步骤 6.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{3}$ 重写成 $3^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6.6.4

约去 $2$ 的公因数。

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解题步骤 6.6.4.1

约去公因数。

解题步骤 6.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{1}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 6.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 7

将 $\frac{1}{\sqrt{2}}$ 乘以 $\frac{\sqrt{2}}{\sqrt{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8

合并和化简分母。

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解题步骤 8.1

将 $\frac{1}{\sqrt{2}}$ 乘以 $\frac{\sqrt{2}}{\sqrt{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8.2

对 $\sqrt{2}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8.3

对 $\sqrt{2}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8.6

将 ${\sqrt{2}}^{2}$ 重写为 $2$ 。

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解题步骤 8.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{2}$ 重写成 $2^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{\frac{2}{2}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8.6.4

约去 $2$ 的公因数。

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解题步骤 8.6.4.1

约去公因数。

解题步骤 8.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 8.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 9

将分子乘以分母的倒数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{2}) & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 10

约去 $0.5$ 的公因数。

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解题步骤 10.1

从 $2$ 中分解出因数 $0.5$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{0.5 (4)}) & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 10.2

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{0.5 \cdot 4}) & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 10.3

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 11

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12

合并和化简分母。

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解题步骤 12.1

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12.2

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12.3

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12.6

将 ${\sqrt{3}}^{2}$ 重写为 $3$ 。

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解题步骤 12.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{3}$ 重写成 $3^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12.6.4

约去 $2$ 的公因数。

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解题步骤 12.6.4.1

约去公因数。

解题步骤 12.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{1}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 12.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 13

将 $\frac{1}{\sqrt{1.5}}$ 乘以 $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{1}{\sqrt{1.5}} \cdot \frac{\sqrt{1.5}}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14

合并和化简分母。

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解题步骤 14.1

将 $\frac{1}{\sqrt{1.5}}$ 乘以 $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{\sqrt{1.5} \sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.2

对 $\sqrt{1.5}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1} \sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.3

对 $\sqrt{1.5}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1} {\sqrt{1.5}}^{1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1 + 1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.6

将 ${\sqrt{1.5}}^{2}$ 重写为 $1.5$ 。

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解题步骤 14.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{1.5}$ 重写成 ${1.5}^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{({1.5}^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{1.5}^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{1.5}^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.6.4

约去 $2$ 的公因数。

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解题步骤 14.6.4.1

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{1.5}^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{1.5}^{1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 14.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{1.5} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 15

计算根。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{1.22474487}{1.5} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 16

用 $1.22474487$ 除以 $1.5$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 17

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18

合并和化简分母。

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解题步骤 18.1

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.2

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.3

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.6

将 ${\sqrt{3}}^{2}$ 重写为 $3$ 。

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解题步骤 18.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{3}$ 重写成 $3^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.6.4

约去 $2$ 的公因数。

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解题步骤 18.6.4.1

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3^{1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 18.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 19

乘以 $[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}]$ 。

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解题步骤 19.1

当且仅当第一个矩阵的列数等于第二个矩阵的行数时，这两个矩阵才可以相乘。在本例中，第一个矩阵是 $3 \times 3$ ，第二个矩阵是 $3 \times 3$ 。

解题步骤 19.2

将第一个矩阵中的每一行乘以第二个矩阵中的每一列。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} \cdot 1 - \frac{\sqrt{1.5}}{4} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \\ \frac{\sqrt{2}}{2} \cdot 1 - \frac{\sqrt{1.5}}{4} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \\ 0 \cdot 1 + 0.81649658 \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & 0 \cdot 0 + 0.81649658 \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & 0 \cdot 0 + 0.81649658 \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 19.3

通过展开所有表达式化简矩阵的每一个元素。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 20

将 $\frac{1}{\sqrt{2}}$ 乘以 $\frac{\sqrt{2}}{\sqrt{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21

合并和化简分母。

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解题步骤 21.1

将 $\frac{1}{\sqrt{2}}$ 乘以 $\frac{\sqrt{2}}{\sqrt{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.2

对 $\sqrt{2}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.3

对 $\sqrt{2}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.6

将 ${\sqrt{2}}^{2}$ 重写为 $2$ 。

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解题步骤 21.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{2}$ 重写成 $2^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.6.4

约去 $2$ 的公因数。

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解题步骤 21.6.4.1

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 21.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 22

将 $\frac{1}{\sqrt{2}}$ 乘以 $\frac{\sqrt{2}}{\sqrt{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23

合并和化简分母。

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解题步骤 23.1

将 $\frac{1}{\sqrt{2}}$ 乘以 $\frac{\sqrt{2}}{\sqrt{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.2

对 $\sqrt{2}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.3

对 $\sqrt{2}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.6

将 ${\sqrt{2}}^{2}$ 重写为 $2$ 。

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解题步骤 23.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{2}$ 重写成 $2^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.6.4

约去 $2$ 的公因数。

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解题步骤 23.6.4.1

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{1}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 23.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 24

将分子乘以分母的倒数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - (0.5 \frac{\sqrt{1.5}}{2}) & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 25

约去 $0.5$ 的公因数。

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解题步骤 25.1

从 $2$ 中分解出因数 $0.5$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - (0.5 \frac{\sqrt{1.5}}{0.5 (4)}) & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 25.2

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - (0.5 \frac{\sqrt{1.5}}{0.5 \cdot 4}) & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 25.3

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 26

将分子乘以分母的倒数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - (0.5 \frac{\sqrt{1.5}}{2}) & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 27

约去 $0.5$ 的公因数。

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解题步骤 27.1

从 $2$ 中分解出因数 $0.5$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - (0.5 \frac{\sqrt{1.5}}{0.5 (4)}) & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 27.2

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - (0.5 \frac{\sqrt{1.5}}{0.5 \cdot 4}) & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 27.3

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 28

将 $\frac{1}{\sqrt{1.5}}$ 乘以 $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{1.5}} \cdot \frac{\sqrt{1.5}}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29

合并和化简分母。

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解题步骤 29.1

将 $\frac{1}{\sqrt{1.5}}$ 乘以 $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{\sqrt{1.5} \sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.2

对 $\sqrt{1.5}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1} \sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.3

对 $\sqrt{1.5}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1} {\sqrt{1.5}}^{1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1 + 1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.6

将 ${\sqrt{1.5}}^{2}$ 重写为 $1.5$ 。

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解题步骤 29.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{1.5}$ 重写成 ${1.5}^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{({1.5}^{\frac{1}{2}})}^{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{1.5}^{\frac{1}{2} \cdot 2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{1.5}^{\frac{2}{2}}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.6.4

约去 $2$ 的公因数。

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解题步骤 29.6.4.1

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{1.5}^{\frac{2}{2}}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{1.5}^{1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 29.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{1.5} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 30

计算根。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{1.22474487}{1.5} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 31

用 $1.22474487$ 除以 $1.5$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 32

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33

合并和化简分母。

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解题步骤 33.1

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.2

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.3

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{\sqrt{3}}^{2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.6

将 ${\sqrt{3}}^{2}$ 重写为 $3$ 。

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解题步骤 33.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{3}$ 重写成 $3^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.6.4

约去 $2$ 的公因数。

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解题步骤 33.6.4.1

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3^{1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 33.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 34

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35

合并和化简分母。

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解题步骤 35.1

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.2

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.3

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.6

将 ${\sqrt{3}}^{2}$ 重写为 $3$ 。

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解题步骤 35.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{3}$ 重写成 $3^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.6.4

约去 $2$ 的公因数。

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解题步骤 35.6.4.1

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{1}} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 35.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \end{array}]$

解题步骤 36

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \end{array}]$

解题步骤 37

合并和化简分母。

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解题步骤 37.1

将 $\frac{1}{\sqrt{3}}$ 乘以 $\frac{\sqrt{3}}{\sqrt{3}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \end{array}]$

解题步骤 37.2

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \end{array}]$

解题步骤 37.3

对 $\sqrt{3}$ 进行 $1$ 次方运算。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \end{array}]$

解题步骤 37.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \end{array}]$

解题步骤 37.5

将 $1$ 和 $1$ 相加。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \end{array}]$

解题步骤 37.6

将 ${\sqrt{3}}^{2}$ 重写为 $3$ 。

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解题步骤 37.6.1

使用 $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ ，将 $\sqrt{3}$ 重写成 $3^{\frac{1}{2}}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \end{array}]$

解题步骤 37.6.2

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \end{array}]$

解题步骤 37.6.3

组合 $\frac{1}{2}$ 和 $2$ 。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}]$

解题步骤 37.6.4

约去 $2$ 的公因数。

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解题步骤 37.6.4.1

约去公因数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}]$

解题步骤 37.6.4.2

重写表达式。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{1}} \end{array}]$

解题步骤 37.6.5

计算指数。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} \end{array}]$

解题步骤 38

乘以 $[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} \end{array}]$ 。

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解题步骤 38.1

当且仅当第一个矩阵的列数等于第二个矩阵的行数时，这两个矩阵才可以相乘。在本例中，第一个矩阵是 $3 \times 3$ ，第二个矩阵是 $3 \times 3$ 。

解题步骤 38.2

将第一个矩阵中的每一行乘以第二个矩阵中的每一列。

$[\begin{array}{c} - \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) - \frac{\sqrt{1.5}}{4} (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & - \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} - \frac{\sqrt{1.5}}{4} (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 0.81649658 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) - \frac{\sqrt{1.5}}{4} (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} - \frac{\sqrt{1.5}}{4} (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 0.81649658 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \\ 0 (- \frac{\sqrt{2}}{2}) + 0.81649658 (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & 0 \frac{\sqrt{2}}{2} + 0.81649658 (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & 0 \cdot 0 + 0.81649658 \cdot 0.81649658 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \end{array}]$

解题步骤 38.3

通过展开所有表达式化简矩阵的每一个元素。

$[\begin{array}{c} 1.92708\overline{3} & 0.92708\overline{3} & 1.08333333 \\ 0.92708\overline{3} & 1.92708\overline{3} & 1.08333333 \\ 1.08333333 & 1.08333333 & 2 \end{array}]$

线性代数 示例

线性代数示例