Find the Inverse [[11,-5],[2,-1]]

$[\begin{array}{c} 11 & - 5 \\ 2 & - 1 \end{array}]$

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 $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$11 \cdot - 1 - 2 \cdot - 5$

Simplify the determinant.

Simplify each term.

Multiply $11$ by $- 1$ .

$- 11 - 2 \cdot - 5$

Multiply $- 2$ by $- 5$ .

$- 11 + 10$

Add $- 11$ and $10$ .

$- 1$

Step 3

Substitute the known values into the formula for the inverse.

$\frac{1}{- 1} [\begin{array}{c} - 1 & 5 \\ - 2 & 11 \end{array}]$

Step 4

Divide $1$ by $- 1$ .

$- [\begin{array}{c} - 1 & 5 \\ - 2 & 11 \end{array}]$

Step 5

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

$[\begin{array}{c} - - 1 & - 1 \cdot 5 \\ - - 2 & - 1 \cdot 11 \end{array}]$

Step 6

Simplify each element in the matrix.

Multiply $- 1$ by $- 1$ .

$[\begin{array}{c} 1 & - 1 \cdot 5 \\ - - 2 & - 1 \cdot 11 \end{array}]$

Multiply $- 1$ by $5$ .

$[\begin{array}{c} 1 & - 5 \\ - - 2 & - 1 \cdot 11 \end{array}]$

Multiply $- 1$ by $- 2$ .

$[\begin{array}{c} 1 & - 5 \\ 2 & - 1 \cdot 11 \end{array}]$

Multiply $- 1$ by $11$ .

$[\begin{array}{c} 1 & - 5 \\ 2 & - 11 \end{array}]$

Find the Inverse [[11,-5],[2,-1]]

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