Linear Algebra Examples

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

Step 1

Add the corresponding elements.

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

Step 2

Simplify each element.

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Step 2.1

Subtract $9$ from $- 5$ .

$[\begin{array}{c} - 14 & - 4 + 3 \\ 7 + 1 & 4 + 2 \end{array}] - [\begin{array}{c} 7 & - 2 \\ - 2 & 8 \end{array}]$

Step 2.2

Add $- 4$ and $3$ .

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

Step 2.3

Add $7$ and $1$ .

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

Step 2.4

Add $4$ and $2$ .

$[\begin{array}{c} - 14 & - 1 \\ 8 & 6 \end{array}] - [\begin{array}{c} 7 & - 2 \\ - 2 & 8 \end{array}]$

Step 3

Subtract the corresponding elements.

$[\begin{array}{c} - 14 - 7 & - 1 + 2 \\ 8 + 2 & 6 - 8 \end{array}]$

Step 4

Simplify each element.

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Step 4.1

Subtract $7$ from $- 14$ .

$[\begin{array}{c} - 21 & - 1 + 2 \\ 8 + 2 & 6 - 8 \end{array}]$

Step 4.2

Add $- 1$ and $2$ .

$[\begin{array}{c} - 21 & 1 \\ 8 + 2 & 6 - 8 \end{array}]$

Step 4.3

Add $8$ and $2$ .

$[\begin{array}{c} - 21 & 1 \\ 10 & 6 - 8 \end{array}]$

Step 4.4

Subtract $8$ from $6$ .

$[\begin{array}{c} - 21 & 1 \\ 10 & - 2 \end{array}]$