Algebra Examples

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

Step 1

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

$determinant [\begin{array}{c} 0 & - 1 \\ - 3 & 1 \end{array}] = | \begin{array}{c} 0 & - 1 \\ - 3 & 1 \end{array} |$

Step 2

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

$(0) (1) + 3 \cdot - 1$

Step 3

Simplify the determinant.

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Simplify each term.

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Multiply $0$ by $1$ .

$0 + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$0 - 3$

Subtract $3$ from $0$ .

$- 3$