LINEAR TRANSFORMATIONS WITH MATRICES  

1. Write the $2 × 2$ matrix associated with horizontal reflection, call it $H$.

   Hint (a):

   In a horizontal reflection, $(x, y) → (−x, y)$.

   Step (a):

   $\left[ \begin{array} { c c } { a } & { b } \\ { c } & { d } \end{array} \right] \left[ \begin{array} { c } { x } \\ { y } \end{array} \right]=\left[ \begin{array} { c } { -x } \\ { y } \end{array} \right]$
   Solve for $a, b, c,$ and $d$.

2. Write the $2 × 2$ matrix associated with vertical reflection, call it $V$.

   Step (b):

   $\left[ \begin{array} { c c } { a } & { b } \\ { c } & { d } \end{array} \right] \left[ \begin{array} { c } { x } \\ { y } \end{array} \right]=\left[ \begin{array} { c } { -x } \\ { y } \end{array} \right]$

3. Compute $HV$. What linear transformation is associated with this matrix?

4. Compute $VH$. Does this matrix create the same linear transformation as $HV$? Explain why or why not.