Question

Find the inverse of the matrix down below in the picture i posted i need help asap

Answer 1

We have the matrix:

`A=\begin{bmatrix}{4} & {-5} \\ {-7} & {9}\end{bmatrix}`

The inverse is given by:

`A^(-1)=\frac{1}{\det\begin{bmatrix}{a} & {b} \\ {c} & {d}\end{bmatrix}}\begin{bmatrix}{d} & {-b} \\ {-c} & {a}\end{bmatrix}`

In this case, a = 4, b = -5, c = -7 and d = 9, Therefore we solve:

`\det A=ad-bc=4\cdot9-(-5)\cdot(-7)=36-35=1`

And

`\begin{gathered} A^(-1)=(1)/(1)\begin{bmatrix}{9} & {-(-5)} \\ {-(-7)} & {4}\end{bmatrix} \\ A^(-1)=1\begin{bmatrix}{9} & {5} \\ {7} & {4}\end{bmatrix} \\ A^(-1)=\begin{bmatrix}{9} & {5} \\ {7} & {4}\end{bmatrix} \end{gathered}`

Answer:

`A^(-1)=\begin{bmatrix}{9} & {5} \\ {7} & {4}\end{bmatrix}`