Finite Math Examples

$[\begin{array}{c} 8 & - 4 \\ 10 & - 5 \end{array}]$

Step 1

Find the determinant.

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Step 1.1

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

$8 \cdot - 5 - 10 \cdot - 4$

Step 1.2

Simplify the determinant.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $8$ by $- 5$ .

$- 40 - 10 \cdot - 4$

Step 1.2.1.2

Multiply $- 10$ by $- 4$ .

$- 40 + 40$

Step 1.2.2

Add $- 40$ and $40$ .

$0$

Step 2

There is no inverse because the determinant is $0$ .