Linear Algebra Examples

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

Step 1

Multiply $2$ by each element of the matrix.

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

Step 2

Simplify each element in the matrix.

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Step 2.1

Multiply $2$ by $1$ .

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

Step 2.2

Multiply $2$ by $2$ .

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

Step 2.3

Multiply $2$ by $- 2$ .

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

Step 2.4

Multiply $2$ by $1$ .

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

Step 3

Multiply $3$ by each element of the matrix.

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

Step 4

Simplify each element in the matrix.

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Step 4.1

Multiply $3$ by $- 5$ .

$[\begin{array}{c} 2 & 4 \\ - 4 & 2 \end{array}] + [\begin{array}{c} - 15 \\ 3 \cdot 3 \end{array}]$

Step 4.2

Multiply $3$ by $3$ .

$[\begin{array}{c} 2 & 4 \\ - 4 & 2 \end{array}] + [\begin{array}{c} - 15 \\ 9 \end{array}]$