Precalculus Examples

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

Step 1

Subtract the corresponding elements.

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

Step 2

Simplify each element of the matrix $[\begin{array}{c} 2 - (- 3) & 1 - (- 3) \\ 4 - (- 5) & 1 - (- 3) \end{array}]$ .

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Simplify $2 - (- 3)$ .

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

Simplify $1 - (- 3)$ .

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

Simplify $4 - (- 5)$ .

$[\begin{array}{c} 5 & 4 \\ 9 & 1 - (- 3) \end{array}]$

Simplify $1 - (- 3)$ .

$[\begin{array}{c} 5 & 4 \\ 9 & 4 \end{array}]$

Step 3

Find the determinant of $[\begin{array}{c} 5 & 4 \\ 9 & 4 \end{array}]$ .

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

$determinant [\begin{array}{c} 5 & 4 \\ 9 & 4 \end{array}] = | \begin{array}{c} 5 & 4 \\ 9 & 4 \end{array} |$

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

$(5) (4) - 9 \cdot 4$

Simplify the determinant.

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Simplify each term.

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Multiply $5$ by $4$ .

$20 - 9 \cdot 4$

Multiply $- 9$ by $4$ .

$20 - 36$

Subtract $36$ from $20$ .

$- 16$

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