Linear Algebra Examples

$[\begin{array}{c} - 4 & 30 + 2 k \\ - 12 & - 10 + 2 k \end{array}]$

Step 1

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

$- 4 (- 10 + 2 k) - (- 12 (30 + 2 k))$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 4 \cdot - 10 - 4 (2 k) - (- 12 (30 + 2 k))$

Step 2.1.2

Multiply $- 4$ by $- 10$ .

$40 - 4 (2 k) - (- 12 (30 + 2 k))$

Step 2.1.3

Multiply $2$ by $- 4$ .

$40 - 8 k - (- 12 (30 + 2 k))$

Step 2.1.4

Apply the distributive property.

$40 - 8 k - (- 12 \cdot 30 - 12 (2 k))$

Step 2.1.5

Multiply $- 12$ by $30$ .

$40 - 8 k - (- 360 - 12 (2 k))$

Step 2.1.6

Multiply $2$ by $- 12$ .

$40 - 8 k - (- 360 - 24 k)$

Step 2.1.7

Apply the distributive property.

$40 - 8 k - - 360 - (- 24 k)$

Step 2.1.8

Multiply $- 1$ by $- 360$ .

$40 - 8 k + 360 - (- 24 k)$

Step 2.1.9

Multiply $- 24$ by $- 1$ .

$40 - 8 k + 360 + 24 k$

Step 2.2

Add $40$ and $360$ .

$- 8 k + 400 + 24 k$

Step 2.3

Add $- 8 k$ and $24 k$ .

$16 k + 400$