Linear Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $3$ by each element of the matrix.

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

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $3$ by $- 2$ .

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

Step 1.2.2

Multiply $3$ by $- 1$ .

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

Step 1.2.3

Multiply $3$ by $1$ .

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

Step 1.2.4

Multiply $3$ by $0$ .

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

Step 1.2.5

Multiply $3$ by $3$ .

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

Step 1.2.6

Multiply $3$ by $- 4$ .

$[\begin{array}{c} - 6 & - 3 \\ 3 & 0 \\ 9 & - 12 \end{array}] - 2 [\begin{array}{c} 0 & 3 \\ 2 & 0 \\ - 4 & - 1 \end{array}]$

Step 1.3

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

$[\begin{array}{c} - 6 & - 3 \\ 3 & 0 \\ 9 & - 12 \end{array}] + [\begin{array}{c} - 2 \cdot 0 & - 2 \cdot 3 \\ - 2 \cdot 2 & - 2 \cdot 0 \\ - 2 \cdot - 4 & - 2 \cdot - 1 \end{array}]$

Step 1.4

Simplify each element in the matrix.

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Step 1.4.1

Multiply $- 2$ by $0$ .

$[\begin{array}{c} - 6 & - 3 \\ 3 & 0 \\ 9 & - 12 \end{array}] + [\begin{array}{c} 0 & - 2 \cdot 3 \\ - 2 \cdot 2 & - 2 \cdot 0 \\ - 2 \cdot - 4 & - 2 \cdot - 1 \end{array}]$

Step 1.4.2

Multiply $- 2$ by $3$ .

$[\begin{array}{c} - 6 & - 3 \\ 3 & 0 \\ 9 & - 12 \end{array}] + [\begin{array}{c} 0 & - 6 \\ - 2 \cdot 2 & - 2 \cdot 0 \\ - 2 \cdot - 4 & - 2 \cdot - 1 \end{array}]$

Step 1.4.3

Multiply $- 2$ by $2$ .

$[\begin{array}{c} - 6 & - 3 \\ 3 & 0 \\ 9 & - 12 \end{array}] + [\begin{array}{c} 0 & - 6 \\ - 4 & - 2 \cdot 0 \\ - 2 \cdot - 4 & - 2 \cdot - 1 \end{array}]$

Step 1.4.4

Multiply $- 2$ by $0$ .

$[\begin{array}{c} - 6 & - 3 \\ 3 & 0 \\ 9 & - 12 \end{array}] + [\begin{array}{c} 0 & - 6 \\ - 4 & 0 \\ - 2 \cdot - 4 & - 2 \cdot - 1 \end{array}]$

Step 1.4.5

Multiply $- 2$ by $- 4$ .

$[\begin{array}{c} - 6 & - 3 \\ 3 & 0 \\ 9 & - 12 \end{array}] + [\begin{array}{c} 0 & - 6 \\ - 4 & 0 \\ 8 & - 2 \cdot - 1 \end{array}]$

Step 1.4.6

Multiply $- 2$ by $- 1$ .

$[\begin{array}{c} - 6 & - 3 \\ 3 & 0 \\ 9 & - 12 \end{array}] + [\begin{array}{c} 0 & - 6 \\ - 4 & 0 \\ 8 & 2 \end{array}]$

Step 2

Add the corresponding elements.

$[\begin{array}{c} - 6 + 0 & - 3 - 6 \\ 3 - 4 & 0 + 0 \\ 9 + 8 & - 12 + 2 \end{array}]$

Step 3

Simplify each element.

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Step 3.1

Add $- 6$ and $0$ .

$[\begin{array}{c} - 6 & - 3 - 6 \\ 3 - 4 & 0 + 0 \\ 9 + 8 & - 12 + 2 \end{array}]$

Step 3.2

Subtract $6$ from $- 3$ .

$[\begin{array}{c} - 6 & - 9 \\ 3 - 4 & 0 + 0 \\ 9 + 8 & - 12 + 2 \end{array}]$

Step 3.3

Subtract $4$ from $3$ .

$[\begin{array}{c} - 6 & - 9 \\ - 1 & 0 + 0 \\ 9 + 8 & - 12 + 2 \end{array}]$

Step 3.4

Add $0$ and $0$ .

$[\begin{array}{c} - 6 & - 9 \\ - 1 & 0 \\ 9 + 8 & - 12 + 2 \end{array}]$

Step 3.5

Add $9$ and $8$ .

$[\begin{array}{c} - 6 & - 9 \\ - 1 & 0 \\ 17 & - 12 + 2 \end{array}]$

Step 3.6

Add $- 12$ and $2$ .

$[\begin{array}{c} - 6 & - 9 \\ - 1 & 0 \\ 17 & - 10 \end{array}]$