The point (x,y) transformerd in the point Q(4x,x-3y) according to the standardbasis. Find the matrices which represent the inverse of the transformation?
You want to set up a transformation matrix so that $\displaystyle \begin{align*} \left[ \begin{matrix} a & b \\ c & d \end{matrix} \right] \left[ \begin{matrix} x \\ y \end{matrix} \right] = \left[ \begin{matrix} 4x \\ x - 3y \end{matrix} \right] \end{align*}$. Can you multiply out the LHS and figure out what a,b,c,d have to be?