Linear Algebra Examples

[\begin{matrix} 9 & 8 7 & 8 \end{matrix}]

$[\begin{array}{c} 9 & 8 \\ 7 & 8 \end{array}]$

Step 1

The determinant of a

2 \times 2

$2 \times 2$ matrix can be found using the formula

∣ ∣ ∣ \begin{matrix} a & b c & d \end{matrix} ∣ ∣ ∣ = a d - c b

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

9 \cdot 8 - 7 \cdot 8

$9 \cdot 8 - 7 \cdot 8$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

9

$9$ by

8

$8$ .

72 - 7 \cdot 8

$72 - 7 \cdot 8$

Step 2.1.2

Multiply

- 7

$- 7$ by

8

$8$ .

72 - 56

$72 - 56$

72 - 56

$72 - 56$

Step 2.2

Subtract

56

$56$ from

72

$72$ .

16

$16$

16

$16$

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