Find the Inverse [[-1,3],[-1,4]]

$[\begin{array}{c} - 1 & 3 \\ - 1 & 4 \end{array}]$

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.

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

$- 1 \cdot 4 - (- 1 \cdot 3)$

Simplify the determinant.

Simplify each term.

Multiply $- 1$ by $4$ .

$- 4 - (- 1 \cdot 3)$

Multiply $- (- 1 \cdot 3)$ .

Multiply $- 1$ by $3$ .

$- 4 - - 3$

Multiply $- 1$ by $- 3$ .

$- 4 + 3$

Add $- 4$ and $3$ .

$- 1$

Step 3

Substitute the known values into the formula for the inverse.

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

Step 4

Divide $1$ by $- 1$ .

$- [\begin{array}{c} 4 & - 3 \\ 1 & - 1 \end{array}]$

Step 5

Multiply $- 1$ by each element of the matrix.

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

Step 6

Simplify each element in the matrix.

Multiply $- 1$ by $4$ .

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

Multiply $- 1$ by $- 3$ .

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

Multiply $- 1$ by $1$ .

$[\begin{array}{c} - 4 & 3 \\ - 1 & - - 1 \end{array}]$

Multiply $- 1$ by $- 1$ .

$[\begin{array}{c} - 4 & 3 \\ - 1 & 1 \end{array}]$

Find the Inverse [[-1,3],[-1,4]]

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