선형 대수 예제

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] - \frac{1}{2} \cdot [\begin{array}{c} - 1 \\ 1 \\ 1 \\ 1 \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] - \frac{1}{2} \cdot [\begin{array}{c} - 1 \\ 1 \\ 1 \\ 1 \end{array}]$

단계 1

각 항을 간단히 합니다.

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단계 1.1

행렬의 각 원소에

- \frac{1}{2}

$- \frac{1}{2}$ 을 곱합니다.

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} - \frac{1}{2} \cdot - 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} - \frac{1}{2} \cdot - 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]$

단계 1.2

행렬의 각 원소를 간단히 합니다.

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단계 1.2.1

- \frac{1}{2} \cdot - 1

$- \frac{1}{2} \cdot - 1$ 을 곱합니다.

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단계 1.2.1.1

- 1

$- 1$ 에

- 1

$- 1$ 을 곱합니다.

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} 1 (\frac{1}{2}) \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} 1 (\frac{1}{2}) \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]$

단계 1.2.1.2

\frac{1}{2}

$\frac{1}{2}$ 에

1

$1$ 을 곱합니다.

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]$

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]$

단계 1.2.2

- 1

$- 1$ 에

1

$1$ 을 곱합니다.

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \cdot 1 \\ - \frac{1}{2} \cdot 1 \end{array}]$

단계 1.2.3

- 1

$- 1$ 에

1

$1$ 을 곱합니다.

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \cdot 1 \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \cdot 1 \end{array}]$

단계 1.2.4

- 1

$- 1$ 에

1

$1$ 을 곱합니다.

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \end{array}]$

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \end{array}]$

[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \end{array}]

$[\begin{array}{c} 6 \\ 4 \\ 6 \\ - 2 \end{array}] + [\begin{array}{c} \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \\ - \frac{1}{2} \end{array}]$

단계 2

해당하는 원소를 더합니다.

[\begin{array}{c} 6 + \frac{1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} 6 + \frac{1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3

Simplify each element.

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단계 3.1

공통 분모를 가지는 분수로

6

$6$ 을 표현하기 위해

\frac{2}{2}

$\frac{2}{2}$ 을 곱합니다.

[\begin{array}{c} 6 \cdot \frac{2}{2} + \frac{1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} 6 \cdot \frac{2}{2} + \frac{1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.2

6

$6$ 와

\frac{2}{2}

$\frac{2}{2}$ 을 묶습니다.

[\begin{array}{c} \frac{6 \cdot 2}{2} + \frac{1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{6 \cdot 2}{2} + \frac{1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.3

공통분모를 가진 분자끼리 묶습니다.

[\begin{array}{c} \frac{6 \cdot 2 + 1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{6 \cdot 2 + 1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.4

분자를 간단히 합니다.

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단계 3.4.1

6

$6$ 에

2

$2$ 을 곱합니다.

[\begin{array}{c} \frac{12 + 1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{12 + 1}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.4.2

12

$12$ 를

1

$1$ 에 더합니다.

[\begin{array}{c} \frac{13}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

[\begin{array}{c} \frac{13}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ 4 - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.5

공통 분모를 가지는 분수로

4

$4$ 을 표현하기 위해

\frac{2}{2}

$\frac{2}{2}$ 을 곱합니다.

[\begin{array}{c} \frac{13}{2} \\ 4 \cdot \frac{2}{2} - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ 4 \cdot \frac{2}{2} - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.6

4

$4$ 와

\frac{2}{2}

$\frac{2}{2}$ 을 묶습니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{4 \cdot 2}{2} - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{4 \cdot 2}{2} - \frac{1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.7

공통분모를 가진 분자끼리 묶습니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{4 \cdot 2 - 1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{4 \cdot 2 - 1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.8

분자를 간단히 합니다.

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단계 3.8.1

4

$4$ 에

2

$2$ 을 곱합니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{8 - 1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{8 - 1}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.8.2

8

$8$ 에서

1

$1$ 을 뺍니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ 6 - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.9

공통 분모를 가지는 분수로

6

$6$ 을 표현하기 위해

\frac{2}{2}

$\frac{2}{2}$ 을 곱합니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ 6 \cdot \frac{2}{2} - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ 6 \cdot \frac{2}{2} - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.10

6

$6$ 와

\frac{2}{2}

$\frac{2}{2}$ 을 묶습니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{6 \cdot 2}{2} - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{6 \cdot 2}{2} - \frac{1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.11

공통분모를 가진 분자끼리 묶습니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{6 \cdot 2 - 1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{6 \cdot 2 - 1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.12

분자를 간단히 합니다.

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단계 3.12.1

6

$6$ 에

2

$2$ 을 곱합니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{12 - 1}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{12 - 1}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.12.2

12

$12$ 에서

1

$1$ 을 뺍니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - 2 - \frac{1}{2} \end{array}]$

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - 2 - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - 2 - \frac{1}{2} \end{array}]$

단계 3.13

공통 분모를 가지는 분수로

- 2

$- 2$ 을 표현하기 위해

\frac{2}{2}

$\frac{2}{2}$ 을 곱합니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - 2 \cdot \frac{2}{2} - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - 2 \cdot \frac{2}{2} - \frac{1}{2} \end{array}]$

단계 3.14

- 2

$- 2$ 와

\frac{2}{2}

$\frac{2}{2}$ 을 묶습니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 2 \cdot 2}{2} - \frac{1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 2 \cdot 2}{2} - \frac{1}{2} \end{array}]$

단계 3.15

공통분모를 가진 분자끼리 묶습니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 2 \cdot 2 - 1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 2 \cdot 2 - 1}{2} \end{array}]$

단계 3.16

분자를 간단히 합니다.

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단계 3.16.1

- 2

$- 2$ 에

2

$2$ 을 곱합니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 4 - 1}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 4 - 1}{2} \end{array}]$

단계 3.16.2

- 4

$- 4$ 에서

1

$1$ 을 뺍니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 5}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 5}{2} \end{array}]$

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 5}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ \frac{- 5}{2} \end{array}]$

단계 3.17

마이너스 부호를 분수 앞으로 보냅니다.

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - \frac{5}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - \frac{5}{2} \end{array}]$

[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - \frac{5}{2} \end{array}]

$[\begin{array}{c} \frac{13}{2} \\ \frac{7}{2} \\ \frac{11}{2} \\ - \frac{5}{2} \end{array}]$