Linear Algebra Examples

$- 5 ([\begin{array}{c} - 2 & 2 \\ 3 & - 3 \\ 1 & 4 \end{array}] + [\begin{array}{c} 5 & 1 \\ - 1 & 6 \\ 8 & 2 \end{array}])$

Step 1

Add the corresponding elements.

$- 5 [\begin{array}{c} - 2 + 5 & 2 + 1 \\ 3 - 1 & - 3 + 6 \\ 1 + 8 & 4 + 2 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $- 2$ and $5$ .

$- 5 [\begin{array}{c} 3 & 2 + 1 \\ 3 - 1 & - 3 + 6 \\ 1 + 8 & 4 + 2 \end{array}]$

Step 2.2

Add $2$ and $1$ .

$- 5 [\begin{array}{c} 3 & 3 \\ 3 - 1 & - 3 + 6 \\ 1 + 8 & 4 + 2 \end{array}]$

Step 2.3

Subtract $1$ from $3$ .

$- 5 [\begin{array}{c} 3 & 3 \\ 2 & - 3 + 6 \\ 1 + 8 & 4 + 2 \end{array}]$

Step 2.4

Add $- 3$ and $6$ .

$- 5 [\begin{array}{c} 3 & 3 \\ 2 & 3 \\ 1 + 8 & 4 + 2 \end{array}]$

Step 2.5

Add $1$ and $8$ .

$- 5 [\begin{array}{c} 3 & 3 \\ 2 & 3 \\ 9 & 4 + 2 \end{array}]$

Step 2.6

Add $4$ and $2$ .

$- 5 [\begin{array}{c} 3 & 3 \\ 2 & 3 \\ 9 & 6 \end{array}]$

Step 3

Multiply $- 5$ by each element of the matrix.

$[\begin{array}{c} - 5 \cdot 3 & - 5 \cdot 3 \\ - 5 \cdot 2 & - 5 \cdot 3 \\ - 5 \cdot 9 & - 5 \cdot 6 \end{array}]$

Step 4

Simplify each element in the matrix.

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Step 4.1

Multiply $- 5$ by $3$ .

$[\begin{array}{c} - 15 & - 5 \cdot 3 \\ - 5 \cdot 2 & - 5 \cdot 3 \\ - 5 \cdot 9 & - 5 \cdot 6 \end{array}]$

Step 4.2

Multiply $- 5$ by $3$ .

$[\begin{array}{c} - 15 & - 15 \\ - 5 \cdot 2 & - 5 \cdot 3 \\ - 5 \cdot 9 & - 5 \cdot 6 \end{array}]$

Step 4.3

Multiply $- 5$ by $2$ .

$[\begin{array}{c} - 15 & - 15 \\ - 10 & - 5 \cdot 3 \\ - 5 \cdot 9 & - 5 \cdot 6 \end{array}]$

Step 4.4

Multiply $- 5$ by $3$ .

$[\begin{array}{c} - 15 & - 15 \\ - 10 & - 15 \\ - 5 \cdot 9 & - 5 \cdot 6 \end{array}]$

Step 4.5

Multiply $- 5$ by $9$ .

$[\begin{array}{c} - 15 & - 15 \\ - 10 & - 15 \\ - 45 & - 5 \cdot 6 \end{array}]$

Step 4.6

Multiply $- 5$ by $6$ .

$[\begin{array}{c} - 15 & - 15 \\ - 10 & - 15 \\ - 45 & - 30 \end{array}]$