Precalculus Examples

$2 ([\begin{array}{c} 2 & - 3 \\ 4 & 1 \\ - 5 & 0 \\ 2 & - 3 \end{array}] - [\begin{array}{c} - 1 & 0 \\ 4 & - 6 \\ - 3 & - 2 \\ 1 & - 7 \end{array}])$

Step 1

Subtract the corresponding elements.

$2 [\begin{array}{c} 2 + 1 & - 3 - 0 \\ 4 - 4 & 1 + 6 \\ - 5 + 3 & 0 + 2 \\ 2 - 1 & - 3 + 7 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $2$ and $1$ .

$2 [\begin{array}{c} 3 & - 3 - 0 \\ 4 - 4 & 1 + 6 \\ - 5 + 3 & 0 + 2 \\ 2 - 1 & - 3 + 7 \end{array}]$

Step 2.2

Subtract $0$ from $- 3$ .

$2 [\begin{array}{c} 3 & - 3 \\ 4 - 4 & 1 + 6 \\ - 5 + 3 & 0 + 2 \\ 2 - 1 & - 3 + 7 \end{array}]$

Step 2.3

Subtract $4$ from $4$ .

$2 [\begin{array}{c} 3 & - 3 \\ 0 & 1 + 6 \\ - 5 + 3 & 0 + 2 \\ 2 - 1 & - 3 + 7 \end{array}]$

Step 2.4

Add $1$ and $6$ .

$2 [\begin{array}{c} 3 & - 3 \\ 0 & 7 \\ - 5 + 3 & 0 + 2 \\ 2 - 1 & - 3 + 7 \end{array}]$

Step 2.5

Add $- 5$ and $3$ .

$2 [\begin{array}{c} 3 & - 3 \\ 0 & 7 \\ - 2 & 0 + 2 \\ 2 - 1 & - 3 + 7 \end{array}]$

Step 2.6

Add $0$ and $2$ .

$2 [\begin{array}{c} 3 & - 3 \\ 0 & 7 \\ - 2 & 2 \\ 2 - 1 & - 3 + 7 \end{array}]$

Step 2.7

Subtract $1$ from $2$ .

$2 [\begin{array}{c} 3 & - 3 \\ 0 & 7 \\ - 2 & 2 \\ 1 & - 3 + 7 \end{array}]$

Step 2.8

Add $- 3$ and $7$ .

$2 [\begin{array}{c} 3 & - 3 \\ 0 & 7 \\ - 2 & 2 \\ 1 & 4 \end{array}]$

Step 3

Multiply $2$ by each element of the matrix.

$[\begin{array}{c} 2 \cdot 3 & 2 \cdot - 3 \\ 2 \cdot 0 & 2 \cdot 7 \\ 2 \cdot - 2 & 2 \cdot 2 \\ 2 \cdot 1 & 2 \cdot 4 \end{array}]$

Step 4

Simplify each element in the matrix.

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Step 4.1

Multiply $2$ by $3$ .

$[\begin{array}{c} 6 & 2 \cdot - 3 \\ 2 \cdot 0 & 2 \cdot 7 \\ 2 \cdot - 2 & 2 \cdot 2 \\ 2 \cdot 1 & 2 \cdot 4 \end{array}]$

Step 4.2

Multiply $2$ by $- 3$ .

$[\begin{array}{c} 6 & - 6 \\ 2 \cdot 0 & 2 \cdot 7 \\ 2 \cdot - 2 & 2 \cdot 2 \\ 2 \cdot 1 & 2 \cdot 4 \end{array}]$

Step 4.3

Multiply $2$ by $0$ .

$[\begin{array}{c} 6 & - 6 \\ 0 & 2 \cdot 7 \\ 2 \cdot - 2 & 2 \cdot 2 \\ 2 \cdot 1 & 2 \cdot 4 \end{array}]$

Step 4.4

Multiply $2$ by $7$ .

$[\begin{array}{c} 6 & - 6 \\ 0 & 14 \\ 2 \cdot - 2 & 2 \cdot 2 \\ 2 \cdot 1 & 2 \cdot 4 \end{array}]$

Step 4.5

Multiply $2$ by $- 2$ .

$[\begin{array}{c} 6 & - 6 \\ 0 & 14 \\ - 4 & 2 \cdot 2 \\ 2 \cdot 1 & 2 \cdot 4 \end{array}]$

Step 4.6

Multiply $2$ by $2$ .

$[\begin{array}{c} 6 & - 6 \\ 0 & 14 \\ - 4 & 4 \\ 2 \cdot 1 & 2 \cdot 4 \end{array}]$

Step 4.7

Multiply $2$ by $1$ .

$[\begin{array}{c} 6 & - 6 \\ 0 & 14 \\ - 4 & 4 \\ 2 & 2 \cdot 4 \end{array}]$

Step 4.8

Multiply $2$ by $4$ .

$[\begin{array}{c} 6 & - 6 \\ 0 & 14 \\ - 4 & 4 \\ 2 & 8 \end{array}]$