Precalculus Examples

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

Combine the similar matrices with each others.

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

Simplify each element of the matrix $[\begin{array}{c} - 4 - 2 & 0 + 0 \\ 2 - 5 & 2 - 4 \end{array}]$ .

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Combine the same size matrices $[\begin{array}{c} - 2 & 0 \\ - 5 & - 4 \end{array}]$ and $[\begin{array}{c} - 4 & 0 \\ 2 & 2 \end{array}]$ by adding the corresponding elements of each.

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

Simplify element $0, 0$ of the matrix.

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

Simplify element $0, 1$ of the matrix.

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

Simplify element $1, 0$ of the matrix.

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

Simplify element $1, 1$ of the matrix.

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

The determinant of $[\begin{array}{c} - 6 & 0 \\ - 3 & - 2 \end{array}]$ is $12$ .

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These are both valid notations for the determinant of a matrix.

$determinant [\begin{array}{c} - 6 & 0 \\ - 3 & - 2 \end{array}] = | \begin{array}{c} - 6 & 0 \\ - 3 & - 2 \end{array} |$

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$(- 6) (- 2) + 3 \cdot 0$

Simplify the determinant.

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Simplify each term.

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Multiply $- 6$ by $- 2$ .

$12 + 3 \cdot 0$

Multiply $3$ by $0$ .

$12 + 0$

Add $12$ and $0$ .

$12$

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