Precalculus Examples

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

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

Step 1

Subtract the corresponding elements.

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

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

Step 2

Simplify each element.

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Step 2.1

Add

- 2

$- 2$ and

4

$4$ .

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

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

Step 2.2

Subtract

0

$0$ from

0

$0$ .

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

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

Step 2.3

Subtract

2

$2$ from

- 5

$- 5$ .

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

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

Step 2.4

Subtract

2

$2$ from

- 4

$- 4$ .

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

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

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

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

Step 3

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

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

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

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

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

$2$ by

- 6

$- 6$ .

- 12 - (- 7 \cdot 0)

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

Step 4.1.2

Multiply

- (- 7 \cdot 0)

$- (- 7 \cdot 0)$ .

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Step 4.1.2.1

Multiply

- 7

$- 7$ by

0

$0$ .

- 12 - 0

$- 12 - 0$

Step 4.1.2.2

Multiply

- 1

$- 1$ by

0

$0$ .

- 12 + 0

$- 12 + 0$

- 12 + 0

$- 12 + 0$

- 12 + 0

$- 12 + 0$

Step 4.2

Add

- 12

$- 12$ and

0

$0$ .

- 12

$- 12$

- 12

$- 12$

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