유한 수학 예제

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 8 & 9 & 10 & 2270 \\ 0 & 1 & - 1 & 1000 \end{array}]$

단계 1

Perform the row operation $R_{2} = R_{2} - 8 R_{1}$ to make the entry at $2, 1$ a $0$ .

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단계 1.1

Perform the row operation $R_{2} = R_{2} - 8 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 8 - 8 \cdot 1 & 9 - 8 \cdot 1 & 10 - 8 \cdot 1 & 2270 - 8 \cdot 26000 \\ 0 & 1 & - 1 & 1000 \end{array}]$

단계 1.2

$R_{2}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 & 1 & 2 & - 205730 \\ 0 & 1 & - 1 & 1000 \end{array}]$

단계 2

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

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단계 2.1

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

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 & 1 & 2 & - 205730 \\ 0 - 0 & 1 - 1 & - 1 - 2 & 1000 + 205730 \end{array}]$

단계 2.2

$R_{3}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 & 1 & 2 & - 205730 \\ 0 & 0 & - 3 & 206730 \end{array}]$

단계 3

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

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단계 3.1

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

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 & 1 & 2 & - 205730 \\ - \frac{1}{3} \cdot 0 & - \frac{1}{3} \cdot 0 & - \frac{1}{3} \cdot - 3 & - \frac{1}{3} \cdot 206730 \end{array}]$

단계 3.2

$R_{3}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 & 1 & 2 & - 205730 \\ 0 & 0 & 1 & - 68910 \end{array}]$

단계 4

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

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단계 4.1

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

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 - 2 \cdot 0 & 1 - 2 \cdot 0 & 2 - 2 \cdot 1 & - 205730 - 2 \cdot - 68910 \\ 0 & 0 & 1 & - 68910 \end{array}]$

단계 4.2

$R_{2}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 1 & 1 & 26000 \\ 0 & 1 & 0 & - 67910 \\ 0 & 0 & 1 & - 68910 \end{array}]$

단계 5

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

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단계 5.1

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

$[\begin{array}{c} 1 - 0 & 1 - 0 & 1 - 1 & 26000 + 68910 \\ 0 & 1 & 0 & - 67910 \\ 0 & 0 & 1 & - 68910 \end{array}]$

단계 5.2

$R_{1}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 1 & 0 & 94910 \\ 0 & 1 & 0 & - 67910 \\ 0 & 0 & 1 & - 68910 \end{array}]$

단계 6

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

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단계 6.1

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

$[\begin{array}{c} 1 - 0 & 1 - 1 & 0 - 0 & 94910 + 67910 \\ 0 & 1 & 0 & - 67910 \\ 0 & 0 & 1 & - 68910 \end{array}]$

단계 6.2

$R_{1}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 0 & 0 & 162820 \\ 0 & 1 & 0 & - 67910 \\ 0 & 0 & 1 & - 68910 \end{array}]$