Linear Algebra Examples

[\begin{array}{c} 12 & 23 \\ 12 & 23 \end{array}]

$[\begin{array}{c} 12 & 23 \\ 12 & 23 \end{array}]$

Step 1

Find the determinant.

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Step 1.1

The determinant of a

2 \times 2

$2 \times 2$ matrix can be found using the formula

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

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

12 \cdot 23 - 12 \cdot 23

$12 \cdot 23 - 12 \cdot 23$

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

12

$12$ by

23

$23$ .

276 - 12 \cdot 23

$276 - 12 \cdot 23$

Step 1.2.1.2

Multiply

- 12

$- 12$ by

23

$23$ .

276 - 276

$276 - 276$

276 - 276

$276 - 276$

Step 1.2.2

Subtract

276

$276$ from

276

$276$ .

0

$0$

0

$0$

0

$0$

Step 2

There is no inverse because the determinant is

0

$0$ .