Linear Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $3$ by each element of the matrix.

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

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $3$ by $3$ .

$[\begin{array}{c} 2 & 3 \\ 1 & 0 \\ 1 & - 3 \end{array}] + [\begin{array}{c} 9 & 3 \cdot - 2 \\ 3 \cdot 1 & 3 \cdot 5 \\ 3 \cdot - 4 & 3 \cdot 3 \end{array}]$

Step 1.2.2

Multiply $3$ by $- 2$ .

$[\begin{array}{c} 2 & 3 \\ 1 & 0 \\ 1 & - 3 \end{array}] + [\begin{array}{c} 9 & - 6 \\ 3 \cdot 1 & 3 \cdot 5 \\ 3 \cdot - 4 & 3 \cdot 3 \end{array}]$

Step 1.2.3

Multiply $3$ by $1$ .

$[\begin{array}{c} 2 & 3 \\ 1 & 0 \\ 1 & - 3 \end{array}] + [\begin{array}{c} 9 & - 6 \\ 3 & 3 \cdot 5 \\ 3 \cdot - 4 & 3 \cdot 3 \end{array}]$

Step 1.2.4

Multiply $3$ by $5$ .

$[\begin{array}{c} 2 & 3 \\ 1 & 0 \\ 1 & - 3 \end{array}] + [\begin{array}{c} 9 & - 6 \\ 3 & 15 \\ 3 \cdot - 4 & 3 \cdot 3 \end{array}]$

Step 1.2.5

Multiply $3$ by $- 4$ .

$[\begin{array}{c} 2 & 3 \\ 1 & 0 \\ 1 & - 3 \end{array}] + [\begin{array}{c} 9 & - 6 \\ 3 & 15 \\ - 12 & 3 \cdot 3 \end{array}]$

Step 1.2.6

Multiply $3$ by $3$ .

$[\begin{array}{c} 2 & 3 \\ 1 & 0 \\ 1 & - 3 \end{array}] + [\begin{array}{c} 9 & - 6 \\ 3 & 15 \\ - 12 & 9 \end{array}]$

Step 2

Add the corresponding elements.

$[\begin{array}{c} 2 + 9 & 3 - 6 \\ 1 + 3 & 0 + 15 \\ 1 - 12 & - 3 + 9 \end{array}]$

Step 3

Simplify each element.

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Step 3.1

Add $2$ and $9$ .

$[\begin{array}{c} 11 & 3 - 6 \\ 1 + 3 & 0 + 15 \\ 1 - 12 & - 3 + 9 \end{array}]$

Step 3.2

Subtract $6$ from $3$ .

$[\begin{array}{c} 11 & - 3 \\ 1 + 3 & 0 + 15 \\ 1 - 12 & - 3 + 9 \end{array}]$

Step 3.3

Add $1$ and $3$ .

$[\begin{array}{c} 11 & - 3 \\ 4 & 0 + 15 \\ 1 - 12 & - 3 + 9 \end{array}]$

Step 3.4

Add $0$ and $15$ .

$[\begin{array}{c} 11 & - 3 \\ 4 & 15 \\ 1 - 12 & - 3 + 9 \end{array}]$

Step 3.5

Subtract $12$ from $1$ .

$[\begin{array}{c} 11 & - 3 \\ 4 & 15 \\ - 11 & - 3 + 9 \end{array}]$

Step 3.6

Add $- 3$ and $9$ .

$[\begin{array}{c} 11 & - 3 \\ 4 & 15 \\ - 11 & 6 \end{array}]$