有限数学示例

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 1 & 1 & 1 & 260 \\ 55000 & 30000 & 90000 & 13000000 \end{array}]$

解题步骤 1

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

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解题步骤 1.1

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

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 1 - 1 & 1 + 2 & 1 - 0 & 260 - 0 \\ 55000 & 30000 & 90000 & 13000000 \end{array}]$

解题步骤 1.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 & 3 & 1 & 260 \\ 55000 & 30000 & 90000 & 13000000 \end{array}]$

解题步骤 2

Perform the row operation $R_{3} = R_{3} - 55000 R_{1}$ to make the entry at $3, 1$ a $0$ .

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解题步骤 2.1

Perform the row operation $R_{3} = R_{3} - 55000 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 & 3 & 1 & 260 \\ 55000 - 55000 \cdot 1 & 30000 - 55000 \cdot - 2 & 90000 - 55000 \cdot 0 & 13000000 - 55000 \cdot 0 \end{array}]$

解题步骤 2.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 & 3 & 1 & 260 \\ 0 & 140000 & 90000 & 13000000 \end{array}]$

解题步骤 3

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 3.1

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

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ \frac{0}{3} & \frac{3}{3} & \frac{1}{3} & \frac{260}{3} \\ 0 & 140000 & 90000 & 13000000 \end{array}]$

解题步骤 3.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 & 1 & \frac{1}{3} & \frac{260}{3} \\ 0 & 140000 & 90000 & 13000000 \end{array}]$

解题步骤 4

Perform the row operation $R_{3} = R_{3} - 140000 R_{2}$ to make the entry at $3, 2$ a $0$ .

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解题步骤 4.1

Perform the row operation $R_{3} = R_{3} - 140000 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 & 1 & \frac{1}{3} & \frac{260}{3} \\ 0 - 140000 \cdot 0 & 140000 - 140000 \cdot 1 & 90000 - 140000 (\frac{1}{3}) & 13000000 - 140000 (\frac{260}{3}) \end{array}]$

解题步骤 4.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 & 1 & \frac{1}{3} & \frac{260}{3} \\ 0 & 0 & \frac{130000}{3} & \frac{2600000}{3} \end{array}]$

解题步骤 5

Multiply each element of $R_{3}$ by $\frac{3}{130000}$ to make the entry at $3, 3$ a $1$ .

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解题步骤 5.1

Multiply each element of $R_{3}$ by $\frac{3}{130000}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 & 1 & \frac{1}{3} & \frac{260}{3} \\ \frac{3}{130000} \cdot 0 & \frac{3}{130000} \cdot 0 & \frac{3}{130000} \cdot \frac{130000}{3} & \frac{3}{130000} \cdot \frac{2600000}{3} \end{array}]$

解题步骤 5.2

化简 $R_{3}$ 。

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 & 1 & \frac{1}{3} & \frac{260}{3} \\ 0 & 0 & 1 & 20 \end{array}]$

解题步骤 6

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

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解题步骤 6.1

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

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 - \frac{1}{3} \cdot 0 & 1 - \frac{1}{3} \cdot 0 & \frac{1}{3} - \frac{1}{3} \cdot 1 & \frac{260}{3} - \frac{1}{3} \cdot 20 \\ 0 & 0 & 1 & 20 \end{array}]$

解题步骤 6.2

化简 $R_{2}$ 。

$[\begin{array}{c} 1 & - 2 & 0 & 0 \\ 0 & 1 & 0 & 80 \\ 0 & 0 & 1 & 20 \end{array}]$

解题步骤 7

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

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解题步骤 7.1

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

$[\begin{array}{c} 1 + 2 \cdot 0 & - 2 + 2 \cdot 1 & 0 + 2 \cdot 0 & 0 + 2 \cdot 80 \\ 0 & 1 & 0 & 80 \\ 0 & 0 & 1 & 20 \end{array}]$

解题步骤 7.2

化简 $R_{1}$ 。

$[\begin{array}{c} 1 & 0 & 0 & 160 \\ 0 & 1 & 0 & 80 \\ 0 & 0 & 1 & 20 \end{array}]$

有限数学 示例

有限数学示例