Linear Algebra Examples

$[\begin{array}{c} 7 & 0 & 9 \\ 9 & - 7 & 4 \\ 0 & 8 & - 7 \end{array}] - [\begin{array}{c} 3 & - 12 & - 10 \\ - 5 & - 2 & 1 \\ 15 & - 14 & 7 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} 7 - 3 & 0 + 12 & 9 + 10 \\ 9 + 5 & - 7 + 2 & 4 - 1 \\ 0 - 15 & 8 + 14 & - 7 - 7 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $3$ from $7$ .

$[\begin{array}{c} 4 & 0 + 12 & 9 + 10 \\ 9 + 5 & - 7 + 2 & 4 - 1 \\ 0 - 15 & 8 + 14 & - 7 - 7 \end{array}]$

Step 2.2

Add $0$ and $12$ .

$[\begin{array}{c} 4 & 12 & 9 + 10 \\ 9 + 5 & - 7 + 2 & 4 - 1 \\ 0 - 15 & 8 + 14 & - 7 - 7 \end{array}]$

Step 2.3

Add $9$ and $10$ .

$[\begin{array}{c} 4 & 12 & 19 \\ 9 + 5 & - 7 + 2 & 4 - 1 \\ 0 - 15 & 8 + 14 & - 7 - 7 \end{array}]$

Step 2.4

Add $9$ and $5$ .

$[\begin{array}{c} 4 & 12 & 19 \\ 14 & - 7 + 2 & 4 - 1 \\ 0 - 15 & 8 + 14 & - 7 - 7 \end{array}]$

Step 2.5

Add $- 7$ and $2$ .

$[\begin{array}{c} 4 & 12 & 19 \\ 14 & - 5 & 4 - 1 \\ 0 - 15 & 8 + 14 & - 7 - 7 \end{array}]$

Step 2.6

Subtract $1$ from $4$ .

$[\begin{array}{c} 4 & 12 & 19 \\ 14 & - 5 & 3 \\ 0 - 15 & 8 + 14 & - 7 - 7 \end{array}]$

Step 2.7

Subtract $15$ from $0$ .

$[\begin{array}{c} 4 & 12 & 19 \\ 14 & - 5 & 3 \\ - 15 & 8 + 14 & - 7 - 7 \end{array}]$

Step 2.8

Add $8$ and $14$ .

$[\begin{array}{c} 4 & 12 & 19 \\ 14 & - 5 & 3 \\ - 15 & 22 & - 7 - 7 \end{array}]$

Step 2.9

Subtract $7$ from $- 7$ .

$[\begin{array}{c} 4 & 12 & 19 \\ 14 & - 5 & 3 \\ - 15 & 22 & - 14 \end{array}]$