유한 수학 예제

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

단계 1

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

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단계 1.1

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

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

단계 1.2

$R_{2}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & - 5 & 4 \\ 0 & 12 & - 3 \end{array}]$

단계 2

Multiply each element of $R_{2}$ by $\frac{1}{12}$ to make the entry at $2, 2$ a $1$ .

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단계 2.1

Multiply each element of $R_{2}$ by $\frac{1}{12}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - 5 & 4 \\ \frac{0}{12} & \frac{12}{12} & \frac{- 3}{12} \end{array}]$

단계 2.2

$R_{2}$ 을 간단히 합니다.

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

단계 3

Perform the row operation $R_{1} = R_{1} + 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

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단계 3.1

Perform the row operation $R_{1} = R_{1} + 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

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

단계 3.2

$R_{1}$ 을 간단히 합니다.

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