Algebra Examples

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

Step 1

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

$5 \cdot - 3 - (- 1 \cdot 3)$

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 $- 3$ .

$- 15 - (- 1 \cdot 3)$

Step 2.1.2

Multiply $- (- 1 \cdot 3)$ .

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Step 2.1.2.1

Multiply $- 1$ by $3$ .

$- 15 - - 3$

Step 2.1.2.2

Multiply $- 1$ by $- 3$ .

$- 15 + 3$

Step 2.2

Add $- 15$ and $3$ .

$- 12$