Precalculus Examples

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

Step 1

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

$5 \cdot 5 - - - 2$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $5$ by $5$ .

$25 - - - 2$

Step 2.1.2

Multiply $- - - 2$ .

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Step 2.1.2.1

Multiply $- 1$ by $- 2$ .

$25 - 1 \cdot 2$

Step 2.1.2.2

Multiply $- 1$ by $2$ .

$25 - 2$

Step 2.2

Subtract $2$ from $25$ .

$23$