Linear Algebra Examples

$[\begin{array}{c} 2 & 2 & 5 \\ 0 & 3 & 6 \\ 1 & 0 & 2 \end{array}] + [\begin{array}{c} 1 & 2 & 0 \\ 0 & 3 & 6 \\ 1 & 0 & 2 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 2 + 1 & 2 + 2 & 5 + 0 \\ 0 + 0 & 3 + 3 & 6 + 6 \\ 1 + 1 & 0 + 0 & 2 + 2 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $2$ and $1$ .

$[\begin{array}{c} 3 & 2 + 2 & 5 + 0 \\ 0 + 0 & 3 + 3 & 6 + 6 \\ 1 + 1 & 0 + 0 & 2 + 2 \end{array}]$

Step 2.2

Add $2$ and $2$ .

$[\begin{array}{c} 3 & 4 & 5 + 0 \\ 0 + 0 & 3 + 3 & 6 + 6 \\ 1 + 1 & 0 + 0 & 2 + 2 \end{array}]$

Step 2.3

Add $5$ and $0$ .

$[\begin{array}{c} 3 & 4 & 5 \\ 0 + 0 & 3 + 3 & 6 + 6 \\ 1 + 1 & 0 + 0 & 2 + 2 \end{array}]$

Step 2.4

Add $0$ and $0$ .

$[\begin{array}{c} 3 & 4 & 5 \\ 0 & 3 + 3 & 6 + 6 \\ 1 + 1 & 0 + 0 & 2 + 2 \end{array}]$

Step 2.5

Add $3$ and $3$ .

$[\begin{array}{c} 3 & 4 & 5 \\ 0 & 6 & 6 + 6 \\ 1 + 1 & 0 + 0 & 2 + 2 \end{array}]$

Step 2.6

Add $6$ and $6$ .

$[\begin{array}{c} 3 & 4 & 5 \\ 0 & 6 & 12 \\ 1 + 1 & 0 + 0 & 2 + 2 \end{array}]$

Step 2.7

Add $1$ and $1$ .

$[\begin{array}{c} 3 & 4 & 5 \\ 0 & 6 & 12 \\ 2 & 0 + 0 & 2 + 2 \end{array}]$

Step 2.8

Add $0$ and $0$ .

$[\begin{array}{c} 3 & 4 & 5 \\ 0 & 6 & 12 \\ 2 & 0 & 2 + 2 \end{array}]$

Step 2.9

Add $2$ and $2$ .

$[\begin{array}{c} 3 & 4 & 5 \\ 0 & 6 & 12 \\ 2 & 0 & 4 \end{array}]$