Finite Math Examples

$[\begin{array}{c} 3 & 2 \\ 4 & 6 \end{array}]$

The inverse of a $2 \times 2$ matrix can be found using the formula $\frac{1}{| A |} [\begin{array}{c} d & - b \\ - c & a \end{array}]$ where $| A |$ is the determinant of $A$ .

If $A = [\begin{array}{c} a & b \\ c & d \end{array}]$ then $A^{- 1} = \frac{1}{| A |} [\begin{array}{c} d & - b \\ - c & a \end{array}]$

The determinant of $[\begin{array}{c} 3 & 2 \\ 4 & 6 \end{array}]$ is $10$ .

Tap for more steps...

These are both valid notations for the determinant of a matrix.

$determinant [\begin{array}{c} 3 & 2 \\ 4 & 6 \end{array}] = | \begin{array}{c} 3 & 2 \\ 4 & 6 \end{array} |$

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

$(3) (6) - 4 \cdot 2$

Simplify the determinant.

Tap for more steps...

Simplify each term.

Tap for more steps...

Multiply $3$ by $6$ .

$18 - 4 \cdot 2$

Multiply $- 4$ by $2$ .

$18 - 8$

Subtract $8$ from $18$ .

$10$

Substitute the known values into the formula for the inverse of a matrix.

$\frac{1}{10} [\begin{array}{c} 6 & - (2) \\ - (4) & 3 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 6 & - (2) \\ - (4) & 3 \end{array}]$ .

Tap for more steps...

Simplify element $0, 1$ by multiplying $- (2)$ .

$\frac{1}{10} [\begin{array}{c} 6 & - 2 \\ - (4) & 3 \end{array}]$

Simplify element $1, 0$ by multiplying $- (4)$ .

$\frac{1}{10} [\begin{array}{c} 6 & - 2 \\ - 4 & 3 \end{array}]$

Multiply $\frac{1}{10}$ by each element of the matrix.

$[\begin{array}{c} \frac{1}{10} \cdot 6 & \frac{1}{10} \cdot - 2 \\ \frac{1}{10} \cdot - 4 & \frac{1}{10} \cdot 3 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} \frac{1}{10} \cdot 6 & \frac{1}{10} \cdot - 2 \\ \frac{1}{10} \cdot - 4 & \frac{1}{10} \cdot 3 \end{array}]$ .

Tap for more steps...

Simplify element $0, 0$ by multiplying $\frac{1}{10} \cdot 6$ .

$[\begin{array}{c} \frac{3}{5} & \frac{1}{10} \cdot - 2 \\ \frac{1}{10} \cdot - 4 & \frac{1}{10} \cdot 3 \end{array}]$

Simplify element $0, 1$ by multiplying $\frac{1}{10} \cdot - 2$ .

$[\begin{array}{c} \frac{3}{5} & - \frac{1}{5} \\ \frac{1}{10} \cdot - 4 & \frac{1}{10} \cdot 3 \end{array}]$

Simplify element $1, 0$ by multiplying $\frac{1}{10} \cdot - 4$ .

$[\begin{array}{c} \frac{3}{5} & - \frac{1}{5} \\ - \frac{2}{5} & \frac{1}{10} \cdot 3 \end{array}]$

Simplify element $1, 1$ by multiplying $\frac{1}{10} \cdot 3$ .

$[\begin{array}{c} \frac{3}{5} & - \frac{1}{5} \\ - \frac{2}{5} & \frac{3}{10} \end{array}]$

Enter YOUR Problem