If $\bf p = \left[ \begin{array} { c } { 1 } \\ { - 2 } \end{array} \right]$ and $M = \left[ \begin{array} { c c } { - 1 } & { - 2 } \\ { 4 } & { 5 } \end{array} \right]$, then $M\mathbf{p} = 3\mathbf{p}$.

1. Determine a vector (or $2 × 1$ matrix) $\bf q = \left[ \begin{array} { c } { 10 } \\ { x } \end{array} \right]$ such that $M\mathbf{p} = 3\bf q$.

   Step (a):

   $M\bf p = \left[ \begin{array} { c } { - 10-2x } \\ { 40+5x } \end{array} \right]$

2. What is $\bf r$ if $M\mathbf{r} = \mathbf{r}$?

   Step (b):

   $\left[ \begin{array} { c c } { - 1 } & { - 2 } \\ { 4 } & { 5 } \end{array} \right] \left[ \begin{array} { c c } { x } \\ { y } \end{array} \right]=\left[ \begin{array} { c } { x } \\ { y } \end{array} \right]$