선형 대수 예제

$[\begin{array}{c} 6 & - 8 & 5 \\ - 9 & 12 & 7 \end{array}]$

단계 1

Multiply each element of $R_{1}$ by $\frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

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단계 1.1

Multiply each element of $R_{1}$ by $\frac{1}{6}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{6}{6} & \frac{- 8}{6} & \frac{5}{6} \\ - 9 & 12 & 7 \end{array}]$

단계 1.2

$R_{1}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & - \frac{4}{3} & \frac{5}{6} \\ - 9 & 12 & 7 \end{array}]$

단계 2

Perform the row operation $R_{2} = R_{2} + 9 R_{1}$ to make the entry at $2, 1$ a $0$ .

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단계 2.1

Perform the row operation $R_{2} = R_{2} + 9 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & \frac{5}{6} \\ - 9 + 9 \cdot 1 & 12 + 9 (- \frac{4}{3}) & 7 + 9 (\frac{5}{6}) \end{array}]$

단계 2.2

$R_{2}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & - \frac{4}{3} & \frac{5}{6} \\ 0 & 0 & \frac{29}{2} \end{array}]$

단계 3

Multiply each element of $R_{2}$ by $\frac{2}{29}$ to make the entry at $2, 3$ a $1$ .

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단계 3.1

Multiply each element of $R_{2}$ by $\frac{2}{29}$ to make the entry at $2, 3$ a $1$ .

$[\begin{array}{c} 1 & - \frac{4}{3} & \frac{5}{6} \\ \frac{2}{29} \cdot 0 & \frac{2}{29} \cdot 0 & \frac{2}{29} \cdot \frac{29}{2} \end{array}]$

단계 3.2

$R_{2}$ 을 간단히 합니다.

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

단계 4

Perform the row operation $R_{1} = R_{1} - \frac{5}{6} R_{2}$ to make the entry at $1, 3$ a $0$ .

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단계 4.1

Perform the row operation $R_{1} = R_{1} - \frac{5}{6} R_{2}$ to make the entry at $1, 3$ a $0$ .

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

단계 4.2

$R_{1}$ 을 간단히 합니다.

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