선형 대수 예제

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

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

단계 1

Perform the row operation

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

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

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

2, 1

$2, 1$ a

0

$0$ .

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

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

단계 1.2

R_{2}

$R_{2}$ 을 간단히 합니다.

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

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

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

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

단계 2

Perform the row operation

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

$R_{3} = R_{3} - R_{1}$ 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} - R_{1}

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

3, 1

$3, 1$ a

0

$0$ .

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

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

단계 2.2

R_{3}

$R_{3}$ 을 간단히 합니다.

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

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

단계 3

Perform the row operation

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

$4, 1$ a

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 3.1

Perform the row operation

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

$4, 1$ a

$0$ .

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

단계 3.2

$R_{4}$ 을 간단히 합니다.

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

단계 4

Perform the row operation

$R_{5} = R_{5} - 2 R_{1}$ to make the entry at

$5, 1$ a

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 4.1

Perform the row operation

$R_{5} = R_{5} - 2 R_{1}$ to make the entry at

$5, 1$ a

$0$ .

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

단계 4.2

$R_{5}$ 을 간단히 합니다.

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

단계 5

Multiply each element of

$R_{2}$ by

$- 1$ to make the entry at

$2, 2$ a

$1$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 5.1

Multiply each element of

$R_{2}$ by

$- 1$ to make the entry at

$2, 2$ a

$1$ .

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

단계 5.2

$R_{2}$ 을 간단히 합니다.

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

단계 6

Perform the row operation

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

$3, 2$ a

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 6.1

Perform the row operation

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

$3, 2$ a

$0$ .

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

단계 6.2

$R_{3}$ 을 간단히 합니다.

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

단계 7

Perform the row operation

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

$4, 2$ a

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 7.1

Perform the row operation

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

$4, 2$ a

$0$ .

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

단계 7.2

$R_{4}$ 을 간단히 합니다.

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

단계 8

Perform the row operation

$R_{5} = R_{5} + R_{2}$ to make the entry at

$5, 2$ a

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 8.1

Perform the row operation

$R_{5} = R_{5} + R_{2}$ to make the entry at

$5, 2$ a

$0$ .

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

단계 8.2

$R_{5}$ 을 간단히 합니다.

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

단계 9

Swap

$R_{4}$ with

$R_{3}$ to put a nonzero entry at

$3, 3$ .

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

단계 10

Multiply each element of

$R_{3}$ by

$- 1$ to make the entry at

$3, 3$ a

$1$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 10.1

Multiply each element of

$R_{3}$ by

$- 1$ to make the entry at

$3, 3$ a

$1$ .

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

단계 10.2

$R_{3}$ 을 간단히 합니다.

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

단계 11

Perform the row operation

$R_{5} = R_{5} + R_{3}$ to make the entry at

$5, 3$ a

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 11.1

Perform the row operation

$R_{5} = R_{5} + R_{3}$ to make the entry at

$5, 3$ a

$0$ .

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

단계 11.2

$R_{5}$ 을 간단히 합니다.

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

단계 12

Perform the row operation

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

$2, 3$ a

$0$ .

자세한 풀이 단계를 보려면 여기를 누르십시오...

단계 12.1

Perform the row operation

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

$2, 3$ a

$0$ .

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

단계 12.2

$R_{2}$ 을 간단히 합니다.

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

단계 13

Perform the row operation

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

$1, 2$ a

$0$ .

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단계 13.1

Perform the row operation

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

$1, 2$ a

$0$ .

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

단계 13.2

$R_{1}$ 을 간단히 합니다.

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