Find the Inverse [[3,6],[2,6]]

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

Step 1

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

Step 2

Find the determinant of $[\begin{array}{c} 3 & 6 \\ 2 & 6 \end{array}]$ .

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

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

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

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

Simplify the determinant.

Simplify each term.

Multiply $3$ by $6$ .

$18 - 2 \cdot 6$

Multiply $- 2$ by $6$ .

$18 - 12$

Subtract $12$ from $18$ .

$6$

Step 3

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

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

Step 4

Simplify each element in the matrix.

Rearrange $- (6)$ .

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

Rearrange $- (2)$ .

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

Step 5

Multiply $\frac{1}{6}$ by each element of the matrix.

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

Step 6

Simplify each element in the matrix.

Rearrange $\frac{1}{6} \cdot 6$ .

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

Rearrange $\frac{1}{6} \cdot - 6$ .

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

Rearrange $\frac{1}{6} \cdot - 2$ .

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

Rearrange $\frac{1}{6} \cdot 3$ .

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

Find the Inverse [[3,6],[2,6]]

Related Questions

Support LCMGCF.com by disabling your adblocker.