Precalculus Examples

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

Combine the similar matrices with each others.

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

Simplify each element of the matrix $[\begin{array}{c} 4 - 4 & - 3 - (- 1) \\ 0 - (- 12) & 1 - (- 2) \end{array}]$ .

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Subtract $[\begin{array}{c} 4 & - 1 \\ - 12 & - 2 \end{array}]$ from $[\begin{array}{c} 4 & - 3 \\ 0 & 1 \end{array}]$ by subtracting the corresponding elements of $[\begin{array}{c} 4 & - 1 \\ - 12 & - 2 \end{array}]$ from each element of $[\begin{array}{c} 4 & - 3 \\ 0 & 1 \end{array}]$ .

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

Simplify element $0, 0$ of the matrix.

$[\begin{array}{c} 0 & - 3 - (- 1) \\ 0 - (- 12) & 1 - (- 2) \end{array}]$

Simplify element $0, 1$ of the matrix.

$[\begin{array}{c} 0 & - 2 \\ 0 - (- 12) & 1 - (- 2) \end{array}]$

Simplify element $1, 0$ of the matrix.

$[\begin{array}{c} 0 & - 2 \\ 12 & 1 - (- 2) \end{array}]$

Simplify element $1, 1$ of the matrix.

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

The determinant of $[\begin{array}{c} 0 & - 2 \\ 12 & 3 \end{array}]$ is $24$ .

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

$determinant [\begin{array}{c} 0 & - 2 \\ 12 & 3 \end{array}] = | \begin{array}{c} 0 & - 2 \\ 12 & 3 \end{array} |$

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

$(0) (3) - 12 \cdot - 2$

Simplify the determinant.

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Simplify each term.

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Multiply $0$ by $3$ to get $0$ .

$0 - 12 \cdot - 2$

Multiply $- 12$ by $- 2$ to get $24$ .

$0 + 24$

Add $0$ and $24$ to get $24$ .

$24$

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