유한 수학 예제

$[\begin{array}{c} 0 & 1 & \frac{5}{7} & - \frac{1}{7} & 0 & \frac{16}{7} \\ 1 & 0 & - \frac{3}{7} & \frac{2}{7} & 0 & \frac{30}{7} \\ 0 & 0 & \frac{13}{7} & \frac{3}{7} & 1 & \frac{220}{7} \end{array}]$

단계 1

Swap $R_{2}$ with $R_{1}$ to put a nonzero entry at $1, 1$ .

$[\begin{array}{c} 1 & 0 & - \frac{3}{7} & \frac{2}{7} & 0 & \frac{30}{7} \\ 0 & 1 & \frac{5}{7} & - \frac{1}{7} & 0 & \frac{16}{7} \\ 0 & 0 & \frac{13}{7} & \frac{3}{7} & 1 & \frac{220}{7} \end{array}]$

단계 2

Multiply each element of $R_{3}$ by $\frac{7}{13}$ to make the entry at $3, 3$ a $1$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 2.1

Multiply each element of $R_{3}$ by $\frac{7}{13}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0 & - \frac{3}{7} & \frac{2}{7} & 0 & \frac{30}{7} \\ 0 & 1 & \frac{5}{7} & - \frac{1}{7} & 0 & \frac{16}{7} \\ \frac{7}{13} \cdot 0 & \frac{7}{13} \cdot 0 & \frac{7}{13} \cdot \frac{13}{7} & \frac{7}{13} \cdot \frac{3}{7} & \frac{7}{13} \cdot 1 & \frac{7}{13} \cdot \frac{220}{7} \end{array}]$

단계 2.2

$R_{3}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 0 & - \frac{3}{7} & \frac{2}{7} & 0 & \frac{30}{7} \\ 0 & 1 & \frac{5}{7} & - \frac{1}{7} & 0 & \frac{16}{7} \\ 0 & 0 & 1 & \frac{3}{13} & \frac{7}{13} & \frac{220}{13} \end{array}]$

단계 3

Perform the row operation $R_{2} = R_{2} - \frac{5}{7} R_{3}$ to make the entry at $2, 3$ a $0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 3.1

Perform the row operation $R_{2} = R_{2} - \frac{5}{7} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 0 & - \frac{3}{7} & \frac{2}{7} & 0 & \frac{30}{7} \\ 0 - \frac{5}{7} \cdot 0 & 1 - \frac{5}{7} \cdot 0 & \frac{5}{7} - \frac{5}{7} \cdot 1 & - \frac{1}{7} - \frac{5}{7} \cdot \frac{3}{13} & 0 - \frac{5}{7} \cdot \frac{7}{13} & \frac{16}{7} - \frac{5}{7} \cdot \frac{220}{13} \\ 0 & 0 & 1 & \frac{3}{13} & \frac{7}{13} & \frac{220}{13} \end{array}]$

단계 3.2

$R_{2}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 0 & - \frac{3}{7} & \frac{2}{7} & 0 & \frac{30}{7} \\ 0 & 1 & 0 & - \frac{4}{13} & - \frac{5}{13} & - \frac{892}{91} \\ 0 & 0 & 1 & \frac{3}{13} & \frac{7}{13} & \frac{220}{13} \end{array}]$

단계 4

Perform the row operation $R_{1} = R_{1} + \frac{3}{7} R_{3}$ to make the entry at $1, 3$ a $0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.1

Perform the row operation $R_{1} = R_{1} + \frac{3}{7} R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 + \frac{3}{7} \cdot 0 & 0 + \frac{3}{7} \cdot 0 & - \frac{3}{7} + \frac{3}{7} \cdot 1 & \frac{2}{7} + \frac{3}{7} \cdot \frac{3}{13} & 0 + \frac{3}{7} \cdot \frac{7}{13} & \frac{30}{7} + \frac{3}{7} \cdot \frac{220}{13} \\ 0 & 1 & 0 & - \frac{4}{13} & - \frac{5}{13} & - \frac{892}{91} \\ 0 & 0 & 1 & \frac{3}{13} & \frac{7}{13} & \frac{220}{13} \end{array}]$

단계 4.2

$R_{1}$ 을 간단히 합니다.

$[\begin{array}{c} 1 & 0 & 0 & \frac{5}{13} & \frac{3}{13} & \frac{150}{13} \\ 0 & 1 & 0 & - \frac{4}{13} & - \frac{5}{13} & - \frac{892}{91} \\ 0 & 0 & 1 & \frac{3}{13} & \frac{7}{13} & \frac{220}{13} \end{array}]$