Question

: Find the inverse of each matrix, if it exists.

7.

$\left[\begin{array}{cc}\mathbf{4}& \mathbf{-}\mathbf{8}\\ \mathbf{-}\mathbf{1}& \mathbf{2}\\ & \end{array}\right]$

Short answer

The inverse of the given matrix does not exist.

Step-by-step solution

­- Description of step.

A square matrix$A$ does not have its inverse if $\left|A\right|=0$.

A square matrix$A$have its inverse if$\left|A\right|\ne 0$.

­- Find the determinant of the given matrix.

The determinant of the given matrix is:

$\begin{array}{c}\left|\begin{array}{cc}4& -8\\ -1& 2\end{array}\right|=\left(4\right)\left(2\right)-\left(-1\right)\left(-8\right)\\ =8-8\\ =0\end{array}$

As the determinant of the given matrix is equal to zero, therefore the inverse of the given matrix does not exist

­- Description of step. 

The inverse of the given matrix does not exist..