Linear Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $- 2$ by each element of the matrix.

$[\begin{array}{c} - 2 \cdot 1 & - 2 \cdot 1 \\ - 2 \cdot 2 & - 2 \cdot 2 \end{array}] + [\begin{array}{c} 3 & 1 \\ 3 & 1 \end{array}]$

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $- 2$ by $1$ .

$[\begin{array}{c} - 2 & - 2 \cdot 1 \\ - 2 \cdot 2 & - 2 \cdot 2 \end{array}] + [\begin{array}{c} 3 & 1 \\ 3 & 1 \end{array}]$

Step 1.2.2

Multiply $- 2$ by $1$ .

$[\begin{array}{c} - 2 & - 2 \\ - 2 \cdot 2 & - 2 \cdot 2 \end{array}] + [\begin{array}{c} 3 & 1 \\ 3 & 1 \end{array}]$

Step 1.2.3

Multiply $- 2$ by $2$ .

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

Step 1.2.4

Multiply $- 2$ by $2$ .

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

Step 2

Add the corresponding elements.

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

Step 3

Simplify each element.

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Step 3.1

Add $- 2$ and $3$ .

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

Step 3.2

Add $- 2$ and $1$ .

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

Step 3.3

Add $- 4$ and $3$ .

$[\begin{array}{c} 1 & - 1 \\ - 1 & - 4 + 1 \end{array}]$

Step 3.4

Add $- 4$ and $1$ .

$[\begin{array}{c} 1 & - 1 \\ - 1 & - 3 \end{array}]$