Algebra 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

Add 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

Subtract

4

$4$ from

- 2

$- 2$ .

[\begin{array}{c} - 6 & 0 + 0 \\ - 5 + 2 & - 4 + 2 \end{array}]

$[\begin{array}{c} - 6 & 0 + 0 \\ - 5 + 2 & - 4 + 2 \end{array}]$

Step 2.2

Add

0

$0$ and

0

$0$ .

[\begin{array}{c} - 6 & 0 \\ - 5 + 2 & - 4 + 2 \end{array}]

$[\begin{array}{c} - 6 & 0 \\ - 5 + 2 & - 4 + 2 \end{array}]$

Step 2.3

Add

- 5

$- 5$ and

2

$2$ .

[\begin{array}{c} - 6 & 0 \\ - 3 & - 4 + 2 \end{array}]

$[\begin{array}{c} - 6 & 0 \\ - 3 & - 4 + 2 \end{array}]$

Step 2.4

Add

- 4

$- 4$ and

2

$2$ .

[\begin{array}{c} - 6 & 0 \\ - 3 & - 2 \end{array}]

$[\begin{array}{c} - 6 & 0 \\ - 3 & - 2 \end{array}]$

[\begin{array}{c} - 6 & 0 \\ - 3 & - 2 \end{array}]

$[\begin{array}{c} - 6 & 0 \\ - 3 & - 2 \end{array}]$

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

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

- 6 \cdot - 2 - (- 3 \cdot 0)

$- 6 \cdot - 2 - (- 3 \cdot 0)$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply

- 6

$- 6$ by

- 2

$- 2$ .

12 - (- 3 \cdot 0)

$12 - (- 3 \cdot 0)$

Step 4.1.2

Multiply

- (- 3 \cdot 0)

$- (- 3 \cdot 0)$ .

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Step 4.1.2.1

Multiply

- 3

$- 3$ 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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