Chapter 6.3, Problem 29E

Finding Standard Matrices for Compositions In Exercises $27-30$, find the standard matrices $A$ and $A^{\prime }$ for $T=T_2\circ T_1$ and $T^{\prime }=T_1\circ T_2$.

$\begin{array}{l}{T}_1:R^2\to R^3,T_1\left(x,y\right)=\left(-2x+3y,x+y,x-2y\right)\\ T_2:R^3\to R^2,T_2\left(x,y,z\right)=\left(x-2y,z+2x\right)\end{array}$