Chapter 4.7, Problem 43E

Finding Transition and Coordinate Matrices In Exercises $41-44$, use a software program or a graphing utility to (a) find the transition matrix from $B$to $B^{\prime }$, (b) find the transition matrix from $B^{\prime }$to $B$, (c) verify that the two transition matrices are inverses of each other, and (d) find the coordinate matrix ${\left[x\right]}_B$, given the coordinate matrix ${\left[x\right]}_{B^{\prime }}$.

$\begin{array}{l}B=\left\{\left(2,0,-1\right),\left(0,-1,3\right),\left(1,-3,-2\right)\right\},\\ B^{\prime }=\left\{\left(0,-1,-3\right),\left(-1,3,-2\right),\left(-3,-2,0\right)\right\},\\ {\left[x\right]}_{B^{\prime }}={\left[\begin{array}{ccc}4& -3& -2\end{array}\right]}^T\end{array}$