Chapter A, Problem 14E

To determine

To prove:

The standard matrix for the composition $T\left(v\right)=T_n\left(T_{n-1}\cdot \cdot \cdot \left(T_3\left(T_2\left(T_1\left(v\right)\right)\right)\right)\cdot \cdot \cdot \right)$ is $A=A_n{A}_{n-1}\cdot \cdot \cdot A_3{A}_2{A}_1$ if the standard matrices of the linear transformations $T_1$, $T_2$, $T_3$ …, $T_n$ are $A_1$, $A_2$, $A_3$, …, $A_n$ respectively.