Linear Algebra Examples

$[\begin{array}{c} 7 & 9 \\ - 2 & - 5 \end{array}]$

Step 1

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

$7 \cdot - 5 - (- 2 \cdot 9)$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $7$ by $- 5$ .

$- 35 - (- 2 \cdot 9)$

Step 2.1.2

Multiply $- (- 2 \cdot 9)$ .

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Step 2.1.2.1

Multiply $- 2$ by $9$ .

$- 35 - - 18$

Step 2.1.2.2

Multiply $- 1$ by $- 18$ .

$- 35 + 18$

Step 2.2

Add $- 35$ and $18$ .

$- 17$