Find the Determinant of the Resulting Matrix

$[\begin{array}{c} - 2 & 0 \\ - 5 & - 4 \end{array}] - [\begin{array}{c} - 4 & 0 \\ 2 & 2 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} - 2 + 4 & 0 - 0 \\ - 5 - 2 & - 4 - 2 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $- 2$ and $4$ .

$[\begin{array}{c} 2 & 0 - 0 \\ - 5 - 2 & - 4 - 2 \end{array}]$

Step 2.2

Subtract $0$ from $0$ .

$[\begin{array}{c} 2 & 0 \\ - 5 - 2 & - 4 - 2 \end{array}]$

Step 2.3

Subtract $2$ from $- 5$ .

$[\begin{array}{c} 2 & 0 \\ - 7 & - 4 - 2 \end{array}]$

Step 2.4

Subtract $2$ from $- 4$ .

$[\begin{array}{c} 2 & 0 \\ - 7 & - 6 \end{array}]$

Step 3

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

$2 \cdot - 6 - (- 7 \cdot 0)$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $2$ by $- 6$ .

$- 12 - (- 7 \cdot 0)$

Step 4.1.2

Multiply $- (- 7 \cdot 0)$ .

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Step 4.1.2.1

Multiply $- 7$ by $0$ .

$- 12 - 0$

Step 4.1.2.2

Multiply $- 1$ by $0$ .

$- 12 + 0$

Step 4.2

Add $- 12$ and $0$ .

$- 12$

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