Chapter 4.7, Problem 54E

CAPSTONE Let $B$ and $B^{\prime }$ be two bases for $R^n$.

(a) When $B=I_n$, write the transition matrix from $B$ to $B^{\prime }$ in terms of $B^{\prime }$.

(b) When $B^{\prime }=I_n$, write the transition matrix from $B$ to $B^{\prime }$ in terms of $B$.

(c) When $B=I_n$, write the transition matrix from $B^{\prime }$ to $B$ in terms of $B^{\prime }$.

(d) When $B^{\prime }=I_n$, write the transition matrix from $B^{\prime }$ to $B$ in terms of $B$.