True or False In Exercises 41 and 42, determine whether

Chapter 6, Problem 41

(choose chapter or problem)

In Exercises 41 and 42, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.

(a) The matrix for a linear transformation A’ relative to the basis B’ is equal to the product \(P^{−1}AP\), where \(P^{−1}\) is the transition matrix from B to B’, A is the matrix for the linear transformation relative to basis B, and P is the transition matrix from B’ to B.

(b) Two matrices that represent the same linear transformation \(T: V \rightarrow V\) with respect to different bases are not necessarily similar.

Text Transcription:

P^-1AP

P^-1

T: V rightarrow V