Question

Find the inverse of the matrix (if it exists). (If the answer does not exist, enter DNE in any cell of the matrix.)

Answer 1

Answer:

$\begin{pmatrix}-15&-28\\ -8&-15\end{pmatrix}$

Step-by-step explanation:

$\begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$

This is the formula we will use. Accordingly:

$=>\frac{1}{\det \begin{pmatrix}-15&28\\ 8&-15\end{pmatrix}}\begin{pmatrix}-15&-28\\ -8&-15\end{pmatrix}$

det represents the determinant

if the determinant is 0 then only the inverse matrix will not exist. So let's find the determinant.

$\det = \left(-15\right)\left(-15\right)-28\cdot \:8\\ = 1$

Now we multiply the following matrix by 1/1:

$\frac{1}{1}\begin{pmatrix}-15&-28\\ -8&-15\end{pmatrix} = \begin{pmatrix}-15&-28\\ -8&-15\end{pmatrix}$