Linear Algebra Examples

$[\begin{array}{c} - 3 & 9 & 9 \\ 1 & 11 & 3 \\ - 11 & - 4 & - 3 \end{array}] + [\begin{array}{c} - 7 & - 5 & 1 \\ - 7 & - 5 & 13 \\ - 1 & - 15 & - 11 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} - 3 - 7 & 9 - 5 & 9 + 1 \\ 1 - 7 & 11 - 5 & 3 + 13 \\ - 11 - 1 & - 4 - 15 & - 3 - 11 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $7$ from $- 3$ .

$[\begin{array}{c} - 10 & 9 - 5 & 9 + 1 \\ 1 - 7 & 11 - 5 & 3 + 13 \\ - 11 - 1 & - 4 - 15 & - 3 - 11 \end{array}]$

Step 2.2

Subtract $5$ from $9$ .

$[\begin{array}{c} - 10 & 4 & 9 + 1 \\ 1 - 7 & 11 - 5 & 3 + 13 \\ - 11 - 1 & - 4 - 15 & - 3 - 11 \end{array}]$

Step 2.3

Add $9$ and $1$ .

$[\begin{array}{c} - 10 & 4 & 10 \\ 1 - 7 & 11 - 5 & 3 + 13 \\ - 11 - 1 & - 4 - 15 & - 3 - 11 \end{array}]$

Step 2.4

Subtract $7$ from $1$ .

$[\begin{array}{c} - 10 & 4 & 10 \\ - 6 & 11 - 5 & 3 + 13 \\ - 11 - 1 & - 4 - 15 & - 3 - 11 \end{array}]$

Step 2.5

Subtract $5$ from $11$ .

$[\begin{array}{c} - 10 & 4 & 10 \\ - 6 & 6 & 3 + 13 \\ - 11 - 1 & - 4 - 15 & - 3 - 11 \end{array}]$

Step 2.6

Add $3$ and $13$ .

$[\begin{array}{c} - 10 & 4 & 10 \\ - 6 & 6 & 16 \\ - 11 - 1 & - 4 - 15 & - 3 - 11 \end{array}]$

Step 2.7

Subtract $1$ from $- 11$ .

$[\begin{array}{c} - 10 & 4 & 10 \\ - 6 & 6 & 16 \\ - 12 & - 4 - 15 & - 3 - 11 \end{array}]$

Step 2.8

Subtract $15$ from $- 4$ .

$[\begin{array}{c} - 10 & 4 & 10 \\ - 6 & 6 & 16 \\ - 12 & - 19 & - 3 - 11 \end{array}]$

Step 2.9

Subtract $11$ from $- 3$ .

$[\begin{array}{c} - 10 & 4 & 10 \\ - 6 & 6 & 16 \\ - 12 & - 19 & - 14 \end{array}]$