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

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Subtract $[\begin{array}{c} - 4 & 0 \\ 2 & 2 \end{array}]$ from $[\begin{array}{c} - 2 & 0 \\ - 5 & - 4 \end{array}]$ by subtracting the corresponding elements of $[\begin{array}{c} - 4 & 0 \\ 2 & 2 \end{array}]$ from each element of $[\begin{array}{c} - 2 & 0 \\ - 5 & - 4 \end{array}]$ .

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

Simplify element $0, 0$ of the matrix.

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

Simplify element $0, 1$ of the matrix.

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

Simplify element $1, 0$ of the matrix.

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

Simplify element $1, 1$ of the matrix.

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

The determinant of $[\begin{array}{c} 2 & 0 \\ - 7 & - 6 \end{array}]$ is $- 12$ .

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

$determinant [\begin{array}{c} 2 & 0 \\ - 7 & - 6 \end{array}] = | \begin{array}{c} 2 & 0 \\ - 7 & - 6 \end{array} |$

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

$(2) (- 6) + 7 \cdot 0$

Simplify the determinant.

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Simplify each term.

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Multiply $2$ by $- 6$ .

$- 12 + 7 \cdot 0$

Multiply $7$ by $0$ .

$- 12 + 0$

Add $- 12$ and $0$ .

$- 12$

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