Linear Algebra Examples

$[\begin{array}{c} 5 & 4 \\ - 3 & 7 \end{array}] + [\begin{array}{c} 9 & 7 \\ 7 & 9 \end{array}] - [\begin{array}{c} 6 & 3 \\ 3 & 6 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 5 + 9 & 4 + 7 \\ - 3 + 7 & 7 + 9 \end{array}] - [\begin{array}{c} 6 & 3 \\ 3 & 6 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $5$ and $9$ .

$[\begin{array}{c} 14 & 4 + 7 \\ - 3 + 7 & 7 + 9 \end{array}] - [\begin{array}{c} 6 & 3 \\ 3 & 6 \end{array}]$

Step 2.2

Add $4$ and $7$ .

$[\begin{array}{c} 14 & 11 \\ - 3 + 7 & 7 + 9 \end{array}] - [\begin{array}{c} 6 & 3 \\ 3 & 6 \end{array}]$

Step 2.3

Add $- 3$ and $7$ .

$[\begin{array}{c} 14 & 11 \\ 4 & 7 + 9 \end{array}] - [\begin{array}{c} 6 & 3 \\ 3 & 6 \end{array}]$

Step 2.4

Add $7$ and $9$ .

$[\begin{array}{c} 14 & 11 \\ 4 & 16 \end{array}] - [\begin{array}{c} 6 & 3 \\ 3 & 6 \end{array}]$

Step 3

Subtract the corresponding elements.

$[\begin{array}{c} 14 - 6 & 11 - 3 \\ 4 - 3 & 16 - 6 \end{array}]$

Step 4

Simplify each element.

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Step 4.1

Subtract $6$ from $14$ .

$[\begin{array}{c} 8 & 11 - 3 \\ 4 - 3 & 16 - 6 \end{array}]$

Step 4.2

Subtract $3$ from $11$ .

$[\begin{array}{c} 8 & 8 \\ 4 - 3 & 16 - 6 \end{array}]$

Step 4.3

Subtract $3$ from $4$ .

$[\begin{array}{c} 8 & 8 \\ 1 & 16 - 6 \end{array}]$

Step 4.4

Subtract $6$ from $16$ .

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