Linear Algebra Examples

$[\begin{array}{c} 5 & 10 \\ 3 & 6 \end{array}]$

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

$5 \cdot 6 - 3 \cdot 10$

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 $5$ by $6$ .

$30 - 3 \cdot 10$

Step 1.2.1.2

Multiply $- 3$ by $10$ .

$30 - 30$

Step 1.2.2

Subtract $30$ from $30$ .

$0$

Step 2

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