Chapter 4.7, Problem 44E

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 ${\left[x\right]}_{B^{\prime }}$.

$\begin{array}{l}B=\left\{\left(1,-1,9\right),\left(-9,1,1\right),\left(1,9,-1\right)\right\},\\ B^{\prime }=\left\{\left(3,0,3\right),\left(-3,3,0\right),\left(0,-3,3\right)\right\},\\ {\left[x\right]}_{B^{\prime }}={\left[\begin{array}{ccc}-5& -4& 1\end{array}\right]}^T\end{array}$