Aljabar Linear Contoh

$[\begin{array}{c} 4 & - 7 & 4 \\ 0 & - 3 & 4 \\ 0 & - 8 & 9 \end{array}] - [\begin{array}{c} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{array}]$

Langkah 1

Kurangkan elemen yang seletak.

$[\begin{array}{c} 4 - 4 & - 7 - 0 & 4 - 0 \\ 0 - 0 & - 3 - 4 & 4 - 0 \\ 0 - 0 & - 8 - 0 & 9 - 4 \end{array}]$

Langkah 2

Simplify each element.

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Langkah 2.1

Kurangi $4$ dengan $4$ .

$[\begin{array}{c} 0 & - 7 - 0 & 4 - 0 \\ 0 - 0 & - 3 - 4 & 4 - 0 \\ 0 - 0 & - 8 - 0 & 9 - 4 \end{array}]$

Langkah 2.2

Kurangi $0$ dengan $- 7$ .

$[\begin{array}{c} 0 & - 7 & 4 - 0 \\ 0 - 0 & - 3 - 4 & 4 - 0 \\ 0 - 0 & - 8 - 0 & 9 - 4 \end{array}]$

Langkah 2.3

Kurangi $0$ dengan $4$ .

$[\begin{array}{c} 0 & - 7 & 4 \\ 0 - 0 & - 3 - 4 & 4 - 0 \\ 0 - 0 & - 8 - 0 & 9 - 4 \end{array}]$

Langkah 2.4

Kurangi $0$ dengan $0$ .

$[\begin{array}{c} 0 & - 7 & 4 \\ 0 & - 3 - 4 & 4 - 0 \\ 0 - 0 & - 8 - 0 & 9 - 4 \end{array}]$

Langkah 2.5

Kurangi $4$ dengan $- 3$ .

$[\begin{array}{c} 0 & - 7 & 4 \\ 0 & - 7 & 4 - 0 \\ 0 - 0 & - 8 - 0 & 9 - 4 \end{array}]$

Langkah 2.6

Kurangi $0$ dengan $4$ .

$[\begin{array}{c} 0 & - 7 & 4 \\ 0 & - 7 & 4 \\ 0 - 0 & - 8 - 0 & 9 - 4 \end{array}]$

Langkah 2.7

Kurangi $0$ dengan $0$ .

$[\begin{array}{c} 0 & - 7 & 4 \\ 0 & - 7 & 4 \\ 0 & - 8 - 0 & 9 - 4 \end{array}]$

Langkah 2.8

Kurangi $0$ dengan $- 8$ .

$[\begin{array}{c} 0 & - 7 & 4 \\ 0 & - 7 & 4 \\ 0 & - 8 & 9 - 4 \end{array}]$

Langkah 2.9

Kurangi $4$ dengan $9$ .

$[\begin{array}{c} 0 & - 7 & 4 \\ 0 & - 7 & 4 \\ 0 & - 8 & 5 \end{array}]$

Langkah 3

Choose the row or column with the most $0$ elements. If there are no $0$ elements choose any row or column. Multiply every element in column $1$ by its cofactor and add.

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Langkah 3.1

Consider the corresponding sign chart.

$| \begin{array}{c} + & - & + \\ - & + & - \\ + & - & + \end{array} |$

Langkah 3.2

The cofactor is the minor with the sign changed if the indices match a $-$ position on the sign chart.

Langkah 3.3

The minor for $a_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} - 7 & 4 \\ - 8 & 5 \end{array} |$

Langkah 3.4

Multiply element $a_{11}$ by its cofactor.

$0 | \begin{array}{c} - 7 & 4 \\ - 8 & 5 \end{array} |$

Langkah 3.5

The minor for $a_{21}$ is the determinant with row $2$ and column $1$ deleted.

$| \begin{array}{c} - 7 & 4 \\ - 8 & 5 \end{array} |$

Langkah 3.6

Multiply element $a_{21}$ by its cofactor.

$0 | \begin{array}{c} - 7 & 4 \\ - 8 & 5 \end{array} |$

Langkah 3.7

The minor for $a_{31}$ is the determinant with row $3$ and column $1$ deleted.

$| \begin{array}{c} - 7 & 4 \\ - 7 & 4 \end{array} |$

Langkah 3.8

Multiply element $a_{31}$ by its cofactor.

$0 | \begin{array}{c} - 7 & 4 \\ - 7 & 4 \end{array} |$

Langkah 3.9

Add the terms together.

$0 | \begin{array}{c} - 7 & 4 \\ - 8 & 5 \end{array} | + 0 | \begin{array}{c} - 7 & 4 \\ - 8 & 5 \end{array} | + 0 | \begin{array}{c} - 7 & 4 \\ - 7 & 4 \end{array} |$

Langkah 4

Kalikan $0$ dengan $| \begin{array}{c} - 7 & 4 \\ - 8 & 5 \end{array} |$ .

$0 + 0 | \begin{array}{c} - 7 & 4 \\ - 8 & 5 \end{array} | + 0 | \begin{array}{c} - 7 & 4 \\ - 7 & 4 \end{array} |$

Langkah 5

Kalikan $0$ dengan $| \begin{array}{c} - 7 & 4 \\ - 8 & 5 \end{array} |$ .

$0 + 0 + 0 | \begin{array}{c} - 7 & 4 \\ - 7 & 4 \end{array} |$

Langkah 6

Kalikan $0$ dengan $| \begin{array}{c} - 7 & 4 \\ - 7 & 4 \end{array} |$ .

$0 + 0 + 0$

Langkah 7

Sederhanakan determinannya.

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Langkah 7.1

Tambahkan $0$ dan $0$ .

$0 + 0$

Langkah 7.2

Tambahkan $0$ dan $0$ .

$0$