有限数学示例

$[\begin{array}{c} 3 & - 2 & 1 & 6 \\ 3 & 1 & - 1 & - 4 \\ - 1 & 2 & - 2 & - 8 \end{array}]$

解题步骤 1

Multiply each element of $R_{1}$ by $\frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

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解题步骤 1.1

Multiply each element of $R_{1}$ by $\frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{3}{3} & \frac{- 2}{3} & \frac{1}{3} & \frac{6}{3} \\ 3 & 1 & - 1 & - 4 \\ - 1 & 2 & - 2 & - 8 \end{array}]$

解题步骤 1.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 3 & 1 & - 1 & - 4 \\ - 1 & 2 & - 2 & - 8 \end{array}]$

解题步骤 2

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

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解题步骤 2.1

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 3 - 3 \cdot 1 & 1 - 3 (- \frac{2}{3}) & - 1 - 3 (\frac{1}{3}) & - 4 - 3 \cdot 2 \\ - 1 & 2 & - 2 & - 8 \end{array}]$

解题步骤 2.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 0 & 3 & - 2 & - 10 \\ - 1 & 2 & - 2 & - 8 \end{array}]$

解题步骤 3

Perform the row operation $R_{3} = R_{3} + R_{1}$ to make the entry at $3, 1$ a $0$ .

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解题步骤 3.1

Perform the row operation $R_{3} = R_{3} + R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 0 & 3 & - 2 & - 10 \\ - 1 + 1 \cdot 1 & 2 - \frac{2}{3} & - 2 + \frac{1}{3} & - 8 + 1 \cdot 2 \end{array}]$

解题步骤 3.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 0 & 3 & - 2 & - 10 \\ 0 & \frac{4}{3} & - \frac{5}{3} & - 6 \end{array}]$

解题步骤 4

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 2$ a $1$ .

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解题步骤 4.1

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ \frac{0}{3} & \frac{3}{3} & \frac{- 2}{3} & \frac{- 10}{3} \\ 0 & \frac{4}{3} & - \frac{5}{3} & - 6 \end{array}]$

解题步骤 4.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 0 & 1 & - \frac{2}{3} & - \frac{10}{3} \\ 0 & \frac{4}{3} & - \frac{5}{3} & - 6 \end{array}]$

解题步骤 5

Perform the row operation $R_{3} = R_{3} - \frac{4}{3} R_{2}$ to make the entry at $3, 2$ a $0$ .

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解题步骤 5.1

Perform the row operation $R_{3} = R_{3} - \frac{4}{3} R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 0 & 1 & - \frac{2}{3} & - \frac{10}{3} \\ 0 - \frac{4}{3} \cdot 0 & \frac{4}{3} - \frac{4}{3} \cdot 1 & - \frac{5}{3} - \frac{4}{3} (- \frac{2}{3}) & - 6 - \frac{4}{3} (- \frac{10}{3}) \end{array}]$

解题步骤 5.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 0 & 1 & - \frac{2}{3} & - \frac{10}{3} \\ 0 & 0 & - \frac{7}{9} & - \frac{14}{9} \end{array}]$

解题步骤 6

Multiply each element of $R_{3}$ by $- \frac{9}{7}$ to make the entry at $3, 3$ a $1$ .

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解题步骤 6.1

Multiply each element of $R_{3}$ by $- \frac{9}{7}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 0 & 1 & - \frac{2}{3} & - \frac{10}{3} \\ - \frac{9}{7} \cdot 0 & - \frac{9}{7} \cdot 0 & - \frac{9}{7} (- \frac{7}{9}) & - \frac{9}{7} (- \frac{14}{9}) \end{array}]$

解题步骤 6.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 0 & 1 & - \frac{2}{3} & - \frac{10}{3} \\ 0 & 0 & 1 & 2 \end{array}]$

解题步骤 7

Perform the row operation $R_{2} = R_{2} + \frac{2}{3} R_{3}$ to make the entry at $2, 3$ a $0$ .

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解题步骤 7.1

Perform the row operation $R_{2} = R_{2} + \frac{2}{3} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & - \frac{2}{3} & \frac{1}{3} & 2 \\ 0 + \frac{2}{3} \cdot 0 & 1 + \frac{2}{3} \cdot 0 & - \frac{2}{3} + \frac{2}{3} \cdot 1 & - \frac{10}{3} + \frac{2}{3} \cdot 2 \\ 0 & 0 & 1 & 2 \end{array}]$

解题步骤 7.2

化简 $R_{2}$ 。

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

解题步骤 8

Perform the row operation $R_{1} = R_{1} - \frac{1}{3} R_{3}$ to make the entry at $1, 3$ a $0$ .

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解题步骤 8.1

Perform the row operation $R_{1} = R_{1} - \frac{1}{3} R_{3}$ to make the entry at $1, 3$ a $0$ .

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

解题步骤 8.2

化简 $R_{1}$ 。

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

解题步骤 9

Perform the row operation $R_{1} = R_{1} + \frac{2}{3} R_{2}$ to make the entry at $1, 2$ a $0$ .

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解题步骤 9.1

Perform the row operation $R_{1} = R_{1} + \frac{2}{3} R_{2}$ to make the entry at $1, 2$ a $0$ .

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

解题步骤 9.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & - 2 \\ 0 & 0 & 1 & 2 \end{array}]$

有限数学 示例

有限数学示例