Algebra Examples

$[\begin{array}{c} \frac{5}{2} & \frac{3}{4} \\ 20 & 4 \end{array}]$

Step 1

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$\frac{5}{2} \cdot 4 - 20 (\frac{3}{4})$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Factor $2$ out of $4$ .

$\frac{5}{2} \cdot (2 (2)) - 20 (\frac{3}{4})$

Step 2.1.1.2

Cancel the common factor.

$\frac{5}{2} \cdot (2 \cdot 2) - 20 (\frac{3}{4})$

Step 2.1.1.3

Rewrite the expression.

$5 \cdot 2 - 20 (\frac{3}{4})$

Step 2.1.2

Multiply $5$ by $2$ .

$10 - 20 (\frac{3}{4})$

Step 2.1.3

Cancel the common factor of $4$ .

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Step 2.1.3.1

Factor $4$ out of $- 20$ .

$10 + 4 (- 5) \frac{3}{4}$

Step 2.1.3.2

Cancel the common factor.

$10 + 4 \cdot - 5 \frac{3}{4}$

Step 2.1.3.3

Rewrite the expression.

$10 - 5 \cdot 3$

Step 2.1.4

Multiply $- 5$ by $3$ .

$10 - 15$

Step 2.2

Subtract $15$ from $10$ .

$- 5$