Evaluating matrix equation A $2x2$ matrix $M$ satisfies the conditions $$M\begin{bmatrix}
       -8 \\
       1
       \end{bmatrix} = \begin{bmatrix}
       3 \\
       8
       \end{bmatrix}$$
and
$$M\begin{bmatrix}
       1 \\
       5
       \end{bmatrix} = \begin{bmatrix}
       -8 \\
       7
       \end{bmatrix}.$$
Evaluate $$M\begin{bmatrix}
       1 \\
       1
       \end{bmatrix}.$$
What is the question essentially asking? Isn't this just a matrix equation?

We know that
$$M\begin{pmatrix}
       -8 & 1 \\
       1 & 5
       \end{pmatrix} = \begin{pmatrix}
       3 &-8\\
       8 & 7
       \end{pmatrix}.$$
Multiply that equation from right by
$$
\begin{pmatrix}
       -8 & 1 \\
       1 & 5
       \end{pmatrix}^{-1}=\frac{1}{-41}\begin{pmatrix}
       5 & -1 \\
       -1 & -8
       \end{pmatrix}
$$
to get $M$.
