Linear Algebra Examples

$[\begin{array}{c} 1 & 2 \\ 2 & 4 \end{array}]$

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

$1 \cdot 4 - 2 \cdot 2$

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 $4$ by $1$ .

$4 - 2 \cdot 2$

Step 1.2.1.2

Multiply $- 2$ by $2$ .

$4 - 4$

Step 1.2.2

Subtract $4$ from $4$ .

$0$

Step 2

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