선형 대수 예제

$[\begin{array}{c} 2 & 0 & - 2 \\ - 3 & 5 & 28 \\ 4 & 1 & 1 \\ 1 & - 2 & - 11 \end{array}]$

단계 1

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

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단계 1.1

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

$[\begin{array}{c} \frac{2}{2} & \frac{0}{2} & \frac{- 2}{2} \\ - 3 & 5 & 28 \\ 4 & 1 & 1 \\ 1 & - 2 & - 11 \end{array}]$

단계 1.2

$R_{1}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 0 & - 1 \\ - 3 & 5 & 28 \\ 4 & 1 & 1 \\ 1 & - 2 & - 11 \end{array}]$

단계 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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단계 2.1

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

$[\begin{array}{c} 1 & 0 & - 1 \\ - 3 + 3 \cdot 1 & 5 + 3 \cdot 0 & 28 + 3 \cdot - 1 \\ 4 & 1 & 1 \\ 1 & - 2 & - 11 \end{array}]$

단계 2.2

$R_{2}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 0 & - 1 \\ 0 & 5 & 25 \\ 4 & 1 & 1 \\ 1 & - 2 & - 11 \end{array}]$

단계 3

Perform the row operation $R_{3} = R_{3} - 4 R_{1}$ to make the entry at $3, 1$ a $0$ .

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단계 3.1

Perform the row operation $R_{3} = R_{3} - 4 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 & - 1 \\ 0 & 5 & 25 \\ 4 - 4 \cdot 1 & 1 - 4 \cdot 0 & 1 - 4 \cdot - 1 \\ 1 & - 2 & - 11 \end{array}]$

단계 3.2

$R_{3}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 0 & - 1 \\ 0 & 5 & 25 \\ 0 & 1 & 5 \\ 1 & - 2 & - 11 \end{array}]$

단계 4

Perform the row operation $R_{4} = R_{4} - R_{1}$ to make the entry at $4, 1$ a $0$ .

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단계 4.1

Perform the row operation $R_{4} = R_{4} - R_{1}$ to make the entry at $4, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 & - 1 \\ 0 & 5 & 25 \\ 0 & 1 & 5 \\ 1 - 1 & - 2 - 0 & - 11 + 1 \end{array}]$

단계 4.2

$R_{4}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 0 & - 1 \\ 0 & 5 & 25 \\ 0 & 1 & 5 \\ 0 & - 2 & - 10 \end{array}]$

단계 5

Multiply each element of $R_{2}$ by $\frac{1}{5}$ to make the entry at $2, 2$ a $1$ .

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단계 5.1

Multiply each element of $R_{2}$ by $\frac{1}{5}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0 & - 1 \\ \frac{0}{5} & \frac{5}{5} & \frac{25}{5} \\ 0 & 1 & 5 \\ 0 & - 2 & - 10 \end{array}]$

단계 5.2

$R_{2}$ 을 간단히 합니다.

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

단계 6

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

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단계 6.1

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

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

단계 6.2

$R_{3}$ 을 간단히 합니다.

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

단계 7

Perform the row operation $R_{4} = R_{4} + 2 R_{2}$ to make the entry at $4, 2$ a $0$ .

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단계 7.1

Perform the row operation $R_{4} = R_{4} + 2 R_{2}$ to make the entry at $4, 2$ a $0$ .

$[\begin{array}{c} 1 & 0 & - 1 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \\ 0 + 2 \cdot 0 & - 2 + 2 \cdot 1 & - 10 + 2 \cdot 5 \end{array}]$

단계 7.2

$R_{4}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 0 & - 1 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}]$