Linear Algebra Examples

[\begin{array}{c} 1 + 1 & 2 + 0 \\ - 1 + 8 & 2 + 2 \end{array}]

$[\begin{array}{c} 1 + 1 & 2 + 0 \\ - 1 + 8 & 2 + 2 \end{array}]$

Step 1

Add

1

$1$ and

1

$1$ .

[\begin{array}{c} 2 & 2 + 0 \\ - 1 + 8 & 2 + 2 \end{array}]

$[\begin{array}{c} 2 & 2 + 0 \\ - 1 + 8 & 2 + 2 \end{array}]$

Step 2

Add

2

$2$ and

0

$0$ .

[\begin{array}{c} 2 & 2 \\ - 1 + 8 & 2 + 2 \end{array}]

$[\begin{array}{c} 2 & 2 \\ - 1 + 8 & 2 + 2 \end{array}]$

Step 3

Add

- 1

$- 1$ and

8

$8$ .

[\begin{array}{c} 2 & 2 \\ 7 & 2 + 2 \end{array}]

$[\begin{array}{c} 2 & 2 \\ 7 & 2 + 2 \end{array}]$

Step 4

Add

2

$2$ and

2

$2$ .

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

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

Step 5

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 4 - 7 \cdot 2

$2 \cdot 4 - 7 \cdot 2$

Step 6

Simplify the determinant.

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Step 6.1

Simplify each term.

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Step 6.1.1

Multiply

2

$2$ by

4

$4$ .

8 - 7 \cdot 2

$8 - 7 \cdot 2$

Step 6.1.2

Multiply

- 7

$- 7$ by

2

$2$ .

8 - 14

$8 - 14$

8 - 14

$8 - 14$

Step 6.2

Subtract

14

$14$ from

8

$8$ .

- 6

$- 6$

- 6

$- 6$

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