Linear Algebra Examples

$(- 2) [\begin{array}{c} 3 \\ 2 \end{array}] + (5) [\begin{array}{c} - 4 \\ 1 \end{array}]$

Step 1

Simplify each term.

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Step 1.1

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

$[\begin{array}{c} - 2 \cdot 3 \\ - 2 \cdot 2 \end{array}] + (5) [\begin{array}{c} - 4 \\ 1 \end{array}]$

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $- 2$ by $3$ .

$[\begin{array}{c} - 6 \\ - 2 \cdot 2 \end{array}] + (5) [\begin{array}{c} - 4 \\ 1 \end{array}]$

Step 1.2.2

Multiply $- 2$ by $2$ .

$[\begin{array}{c} - 6 \\ - 4 \end{array}] + (5) [\begin{array}{c} - 4 \\ 1 \end{array}]$

Step 1.3

Multiply $5$ by each element of the matrix.

$[\begin{array}{c} - 6 \\ - 4 \end{array}] + [\begin{array}{c} 5 \cdot - 4 \\ 5 \cdot 1 \end{array}]$

Step 1.4

Simplify each element in the matrix.

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Step 1.4.1

Multiply $5$ by $- 4$ .

$[\begin{array}{c} - 6 \\ - 4 \end{array}] + [\begin{array}{c} - 20 \\ 5 \cdot 1 \end{array}]$

Step 1.4.2

Multiply $5$ by $1$ .

$[\begin{array}{c} - 6 \\ - 4 \end{array}] + [\begin{array}{c} - 20 \\ 5 \end{array}]$

Step 2

Add the corresponding elements.

$[\begin{array}{c} - 6 - 20 \\ - 4 + 5 \end{array}]$

Step 3

Simplify each element.

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Step 3.1

Subtract $20$ from $- 6$ .

$[\begin{array}{c} - 26 \\ - 4 + 5 \end{array}]$

Step 3.2

Add $- 4$ and $5$ .

$[\begin{array}{c} - 26 \\ 1 \end{array}]$