IMPOSSIBLE SYSTEMS

1. Use your graphing calculator to try to solve: $\left. \begin{array} [t] { r } { 2 x - y = 3 } \\ { 4 x - 2 y = 5 } \end{array} \right.$

   Step (a):

   $\left[ \begin{array} { l } { x } \\ { y } \end{array} \right] = \left[ \begin{array} { l l } { 2 } & { - 1 } \\ { 4 } & { - 2 } \end{array} \right] ^ { - 1 } \left[ \begin{array} { l } { 3 } \\ { 5 } \end{array} \right]$

2. What happened?

   Hint (b):

   You should have gotten an error message.

3. Try to find the inverse of $\left[ \begin{array} { c c } { 2 } & { - 1 } \\ { 4 } & { - 2 } \end{array} \right]$ as you did earlier by hand in 12-9. What goes wrong?

   Step (c):

   $\left[ \begin{array} { l l } { 2 } & { - 1 } \\ { 4 } & { - 2 } \end{array} \right] \left[ \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right] = \left[ \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right]$