Finite Math Examples

$[\begin{array}{c} 0.27 & 0.07 \\ 0.32 & 0.13 \end{array}]$

Step 1

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

Step 2

Find the determinant.

Tap for more steps...

Step 2.1

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

$0.27 \cdot 0.13 - 0.32 \cdot 0.07$

Step 2.2

Simplify the determinant.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

Multiply $0.27$ by $0.13$ .

$0.0351 - 0.32 \cdot 0.07$

Step 2.2.1.2

Multiply $- 0.32$ by $0.07$ .

$0.0351 - 0.0224$

Step 2.2.2

Subtract $0.0224$ from $0.0351$ .

$0.0127$

Step 3

Since the determinant is non-zero, the inverse exists.

Step 4

Substitute the known values into the formula for the inverse.

$\frac{1}{0.0127} [\begin{array}{c} 0.13 & - 0.07 \\ - 0.32 & 0.27 \end{array}]$

Step 5

Divide $1$ by $0.0127$ .

$78.74015748 [\begin{array}{c} 0.13 & - 0.07 \\ - 0.32 & 0.27 \end{array}]$

Step 6

Multiply $78.74015748$ by each element of the matrix.

$[\begin{array}{c} 78.74015748 \cdot 0.13 & 78.74015748 \cdot - 0.07 \\ 78.74015748 \cdot - 0.32 & 78.74015748 \cdot 0.27 \end{array}]$

Step 7

Simplify each element in the matrix.

Tap for more steps...

Step 7.1

Multiply $78.74015748$ by $0.13$ .

$[\begin{array}{c} 10.23622047 & 78.74015748 \cdot - 0.07 \\ 78.74015748 \cdot - 0.32 & 78.74015748 \cdot 0.27 \end{array}]$

Step 7.2

Multiply $78.74015748$ by $- 0.07$ .

$[\begin{array}{c} 10.23622047 & - 5.51181102 \\ 78.74015748 \cdot - 0.32 & 78.74015748 \cdot 0.27 \end{array}]$

Step 7.3

Multiply $78.74015748$ by $- 0.32$ .

$[\begin{array}{c} 10.23622047 & - 5.51181102 \\ - 25.19685039 & 78.74015748 \cdot 0.27 \end{array}]$

Step 7.4

Multiply $78.74015748$ by $0.27$ .

$[\begin{array}{c} 10.23622047 & - 5.51181102 \\ - 25.19685039 & 21.25984251 \end{array}]$