Solved: Let B = {(1, 2), (1, 1)} and B = {(4, 1), (0,

Chapter 6, Problem 15

(choose chapter or problem)

Let B = {(1, 2), (−1, −1)} and B = {(−4, 1), (0, 2)} be bases for \(R^{2}\), and let

\(A=\left[\begin{array}{rr} 2 & 1 \\ 0 & -1 \end{array}\right] \)

be the matrix for \(T: R^{2} \rightarrow R^{2}\) relative to B.

(a) Find the transition matrix P from B’ to B.

(b) Use the matrices P and A to find \([v]_{B}\) and \([T(v)]_{B}\), where \([v]_{B} = [−1 4]^{T}\).

(c) Find \(P^{−1}\) and A’ (the matrix for T relative to B’).

(d) Find \([T(v)]_{B’}\) two ways.

Text Transcription:

R^2

T: R^2 rightarrow R^2

[v]_b

[T(v)]_B

[v]_b’ = [-1 4]^T

P^-1

[T(v)]_B’