Chapter 6 - Linear Transformations - 6.5 The Matrix of a Linear Transformation - True-False Review - Page 426: b

False

A matrix representation of $T$ relative to the bases $B$ and $C$ is given by $[T]_B^C$ , then $B$ shows a basis for $V$ and $C$ shows a basis for $W$. So, a matrix representation of $T$ relative to the bases $V$ and $B$ is given by $[T]_C^B$ , then $B$ shows a basis for $W$ and $C$ shows a basis for $V$, which is not true. Therefore, the given statement is false.