Algebra Examples

$[\begin{array}{c} 5 & \frac{- 1}{3} \\ 30 & 2 \end{array}]$

Step 1

Move the negative in front of the fraction.

$[\begin{array}{c} 5 & - \frac{1}{3} \\ 30 & 2 \end{array}]$

Step 2

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

$5 \cdot 2 - 30 (- \frac{1}{3})$

Step 3

Simplify the determinant.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $5$ by $2$ .

$10 - 30 (- \frac{1}{3})$

Step 3.1.2

Cancel the common factor of $3$ .

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Step 3.1.2.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$10 - 30 (\frac{- 1}{3})$

Step 3.1.2.2

Factor $3$ out of $- 30$ .

$10 + 3 (- 10) \frac{- 1}{3}$

Step 3.1.2.3

Cancel the common factor.

$10 + 3 \cdot - 10 \frac{- 1}{3}$

Step 3.1.2.4

Rewrite the expression.

$10 - 10 \cdot - 1$

Step 3.1.3

Multiply $- 10$ by $- 1$ .

$10 + 10$

Step 3.2

Add $10$ and $10$ .

$20$