Precalculus Examples

[\begin{array}{c} 2 & 4 \\ 6 & 8 \end{array}] + [\begin{array}{c} 1 & 2 \\ 3 & 4 \end{array}]

$[\begin{array}{c} 2 & 4 \\ 6 & 8 \end{array}] + [\begin{array}{c} 1 & 2 \\ 3 & 4 \end{array}]$

Step 1

Add the corresponding elements.

[\begin{array}{c} 2 + 1 & 4 + 2 \\ 6 + 3 & 8 + 4 \end{array}]

$[\begin{array}{c} 2 + 1 & 4 + 2 \\ 6 + 3 & 8 + 4 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add

2

$2$ and

1

$1$ .

[\begin{array}{c} 3 & 4 + 2 \\ 6 + 3 & 8 + 4 \end{array}]

$[\begin{array}{c} 3 & 4 + 2 \\ 6 + 3 & 8 + 4 \end{array}]$

Step 2.2

Add

4

$4$ and

2

$2$ .

[\begin{array}{c} 3 & 6 \\ 6 + 3 & 8 + 4 \end{array}]

$[\begin{array}{c} 3 & 6 \\ 6 + 3 & 8 + 4 \end{array}]$

Step 2.3

Add

6

$6$ and

3

$3$ .

[\begin{array}{c} 3 & 6 \\ 9 & 8 + 4 \end{array}]

$[\begin{array}{c} 3 & 6 \\ 9 & 8 + 4 \end{array}]$

Step 2.4

Add

8

$8$ and

4

$4$ .

[\begin{array}{c} 3 & 6 \\ 9 & 12 \end{array}]

$[\begin{array}{c} 3 & 6 \\ 9 & 12 \end{array}]$

[\begin{array}{c} 3 & 6 \\ 9 & 12 \end{array}]

$[\begin{array}{c} 3 & 6 \\ 9 & 12 \end{array}]$

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

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

3 \cdot 12 - 9 \cdot 6

$3 \cdot 12 - 9 \cdot 6$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply

3

$3$ by

12

$12$ .

36 - 9 \cdot 6

$36 - 9 \cdot 6$

Step 4.1.2

Multiply

- 9

$- 9$ by

6

$6$ .

36 - 54

$36 - 54$

36 - 54

$36 - 54$

Step 4.2

Subtract

54

$54$ from

36

$36$ .

- 18

$- 18$

- 18

$- 18$

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