Find the Inverse [[1,-7],[7,-50]]

$[\begin{array}{c} 1 & - 7 \\ 7 & - 50 \end{array}]$

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

$1 \cdot - 50 - 7 \cdot - 7$

Simplify the determinant.

Simplify each term.

Multiply $- 50$ by $1$ .

$- 50 - 7 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$- 50 + 49$

Add $- 50$ and $49$ .

$- 1$

Step 3

Substitute the known values into the formula for the inverse.

$\frac{1}{- 1} [\begin{array}{c} - 50 & 7 \\ - 7 & 1 \end{array}]$

Step 4

Divide $1$ by $- 1$ .

$- [\begin{array}{c} - 50 & 7 \\ - 7 & 1 \end{array}]$

Step 5

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

$[\begin{array}{c} - - 50 & - 1 \cdot 7 \\ - - 7 & - 1 \cdot 1 \end{array}]$

Step 6

Simplify each element in the matrix.

Multiply $- 1$ by $- 50$ .

$[\begin{array}{c} 50 & - 1 \cdot 7 \\ - - 7 & - 1 \cdot 1 \end{array}]$

Multiply $- 1$ by $7$ .

$[\begin{array}{c} 50 & - 7 \\ - - 7 & - 1 \cdot 1 \end{array}]$

Multiply $- 1$ by $- 7$ .

$[\begin{array}{c} 50 & - 7 \\ 7 & - 1 \cdot 1 \end{array}]$

Multiply $- 1$ by $1$ .

$[\begin{array}{c} 50 & - 7 \\ 7 & - 1 \end{array}]$

Find the Inverse [[1,-7],[7,-50]]

Related Questions

Support LCMGCF.com by disabling your adblocker.