Chapter 4.CR, Problem 69CR

Finding transition and Coordinate Matrices In Exercises $69-72$, (a) find the transition matrix from $B$ to $B^{\prime }$, (b) find the two transition matrix from $B^{\prime }$ to $B$, (c) Verify that the transition matrices are inverses of each other, and (d) Find the coordinate matrix ${\left[x\right]}_{B^{\prime }}$, given the coordinate matrix ${\left[x\right]}_B$.

$B=\left\{\left(-2,1\right),\left(1,-1\right)\right\}$, $B^{\prime }=\left\{\left(0,2\right),\left(1,1\right)\right\}$, ${\left[x\right]}_B={\left[\begin{array}{cc}6& -6\end{array}\right]}^T$