Precalculus Examples

$[\begin{array}{c} 1 + 1 & 2 + 0 \\ - 1 + 8 & 2 + 2 \end{array}]$

Step 1

Add $1$ and $1$ .

$[\begin{array}{c} 2 & 2 + 0 \\ - 1 + 8 & 2 + 2 \end{array}]$

Step 2

Add $2$ and $0$ .

$[\begin{array}{c} 2 & 2 \\ - 1 + 8 & 2 + 2 \end{array}]$

Step 3

Add $- 1$ and $8$ .

$[\begin{array}{c} 2 & 2 \\ 7 & 2 + 2 \end{array}]$

Step 4

Add $2$ and $2$ .

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

Step 5

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

$2 \cdot 4 - 7 \cdot 2$

Step 6

Simplify the determinant.

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Step 6.1

Simplify each term.

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Step 6.1.1

Multiply $2$ by $4$ .

$8 - 7 \cdot 2$

Step 6.1.2

Multiply $- 7$ by $2$ .

$8 - 14$

Step 6.2

Subtract $14$ from $8$ .

$- 6$

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