Algebra Examples

$[\begin{array}{c} \frac{1}{2} & \frac{1}{6} \\ - \frac{11}{4} & \frac{11}{12} \end{array}]$

Step 1

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

$\frac{1}{2} \cdot \frac{11}{12} - (- \frac{11}{4} \cdot \frac{1}{6})$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $\frac{1}{2} \cdot \frac{11}{12}$ .

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Step 2.1.1.1

Multiply $\frac{1}{2}$ by $\frac{11}{12}$ .

$\frac{11}{2 \cdot 12} - (- \frac{11}{4} \cdot \frac{1}{6})$

Step 2.1.1.2

Multiply $2$ by $12$ .

$\frac{11}{24} - (- \frac{11}{4} \cdot \frac{1}{6})$

Step 2.1.2

Multiply $- \frac{11}{4} \cdot \frac{1}{6}$ .

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Step 2.1.2.1

Multiply $\frac{1}{6}$ by $\frac{11}{4}$ .

$\frac{11}{24} - - \frac{11}{6 \cdot 4}$

Step 2.1.2.2

Multiply $6$ by $4$ .

$\frac{11}{24} - - \frac{11}{24}$

Step 2.1.3

Multiply $- - \frac{11}{24}$ .

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Step 2.1.3.1

Multiply $- 1$ by $- 1$ .

$\frac{11}{24} + 1 (\frac{11}{24})$

Step 2.1.3.2

Multiply $\frac{11}{24}$ by $1$ .

$\frac{11}{24} + \frac{11}{24}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{11 + 11}{24}$

Step 2.3

Add $11$ and $11$ .

$\frac{22}{24}$

Step 2.4

Cancel the common factor of $22$ and $24$ .

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Step 2.4.1

Factor $2$ out of $22$ .

$\frac{2 (11)}{24}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $24$ .

$\frac{2 \cdot 11}{2 \cdot 12}$

Step 2.4.2.2

Cancel the common factor.

$\frac{2 \cdot 11}{2 \cdot 12}$

Step 2.4.2.3

Rewrite the expression.

$\frac{11}{12}$