선형 대수 예제

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}]$

단계 1

Perform the row operation

R_{2} = R_{2} - 4 R_{1}

$R_{2} = R_{2} - 4 R_{1}$ to make the entry at

2, 1

$2, 1$ a

0

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 1.1

Perform the row operation

R_{2} = R_{2} - 4 R_{1}

$R_{2} = R_{2} - 4 R_{1}$ to make the entry at

2, 1

$2, 1$ a

0

$0$ .

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 - 4 \cdot 1 & 5 - 4 \cdot 2 & 6 - 4 \cdot 3 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 4 - 4 \cdot 1 & 5 - 4 \cdot 2 & 6 - 4 \cdot 3 \\ 7 & 8 & 9 \end{array}]$

단계 1.2

R_{2}

$R_{2}$ 을 간단히 합니다.

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 3 & - 6 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & - 3 & - 6 \\ 7 & 8 & 9 \end{array}]$

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 3 & - 6 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & - 3 & - 6 \\ 7 & 8 & 9 \end{array}]$

단계 2

Perform the row operation

R_{3} = R_{3} - 7 R_{1}

$R_{3} = R_{3} - 7 R_{1}$ to make the entry at

3, 1

$3, 1$ a

0

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 2.1

Perform the row operation

R_{3} = R_{3} - 7 R_{1}

$R_{3} = R_{3} - 7 R_{1}$ to make the entry at

3, 1

$3, 1$ a

0

$0$ .

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 3 & - 6 7 - 7 \cdot 1 & 8 - 7 \cdot 2 & 9 - 7 \cdot 3 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & - 3 & - 6 \\ 7 - 7 \cdot 1 & 8 - 7 \cdot 2 & 9 - 7 \cdot 3 \end{array}]$

단계 2.2

R_{3}

$R_{3}$ 을 간단히 합니다.

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 3 & - 6 0 & - 6 & - 12 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & - 3 & - 6 \\ 0 & - 6 & - 12 \end{array}]$

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 3 & - 6 0 & - 6 & - 12 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & - 3 & - 6 \\ 0 & - 6 & - 12 \end{array}]$

단계 3

Multiply each element of

R_{2}

$R_{2}$ by

- \frac{1}{3}

$- \frac{1}{3}$ to make the entry at

2, 2

$2, 2$ a

1

$1$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 3.1

Multiply each element of

R_{2}

$R_{2}$ by

- \frac{1}{3}

$- \frac{1}{3}$ to make the entry at

2, 2

$2, 2$ a

1

$1$ .

⎡ ⎢ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 - \frac{1}{3} \cdot 0 & - \frac{1}{3} \cdot - 3 & - \frac{1}{3} \cdot - 6 0 & - 6 & - 12 \end{matrix} ⎤ ⎥ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ - \frac{1}{3} \cdot 0 & - \frac{1}{3} \cdot - 3 & - \frac{1}{3} \cdot - 6 \\ 0 & - 6 & - 12 \end{array}]$

단계 3.2

R_{2}

$R_{2}$ 을 간단히 합니다.

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 2 0 & - 6 & - 12 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & - 6 & - 12 \end{array}]$

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 2 0 & - 6 & - 12 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & - 6 & - 12 \end{array}]$

단계 4

Perform the row operation

R_{3} = R_{3} + 6 R_{2}

$R_{3} = R_{3} + 6 R_{2}$ to make the entry at

3, 2

$3, 2$ a

0

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.1

Perform the row operation

R_{3} = R_{3} + 6 R_{2}

$R_{3} = R_{3} + 6 R_{2}$ to make the entry at

3, 2

$3, 2$ a

0

$0$ .

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 2 0 + 6 \cdot 0 & - 6 + 6 \cdot 1 & - 12 + 6 \cdot 2 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 + 6 \cdot 0 & - 6 + 6 \cdot 1 & - 12 + 6 \cdot 2 \end{array}]$

단계 4.2

R_{3}

$R_{3}$ 을 간단히 합니다.

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 2 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}]$

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 2 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}]$

단계 5

Perform the row operation

R_{1} = R_{1} - 2 R_{2}

$R_{1} = R_{1} - 2 R_{2}$ to make the entry at

1, 2

$1, 2$ a

0

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 5.1

Perform the row operation

R_{1} = R_{1} - 2 R_{2}

$R_{1} = R_{1} - 2 R_{2}$ to make the entry at

1, 2

$1, 2$ a

0

$0$ .

⎡ ⎢ ⎣ \begin{matrix} 1 - 2 \cdot 0 & 2 - 2 \cdot 1 & 3 - 2 \cdot 2 0 & 1 & 2 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

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

단계 5.2

R_{1}

$R_{1}$ 을 간단히 합니다.

⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & - 1 0 & 1 & 2 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

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

⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & - 1 0 & 1 & 2 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

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