Finite Math Examples

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

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 $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$2 (\frac{1}{2}) - - - 1$

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

Cancel the common factor of $2$ .

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Step 1.2.1.1.1

Cancel the common factor.

$2 (\frac{1}{2}) - - - 1$

Step 1.2.1.1.2

Rewrite the expression.

$1 - - - 1$

Step 1.2.1.2

Multiply $- - - 1$ .

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Step 1.2.1.2.1

Multiply $- 1$ by $- 1$ .

$1 - 1 \cdot 1$

Step 1.2.1.2.2

Multiply $- 1$ by $1$ .

$1 - 1$

Step 1.2.2

Subtract $1$ from $1$ .

$0$

Step 2

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