1.) Let B {(1,1), (-2,3)}, and B' = {(1,-1), (0,1)} be bases for R?, and let A = | [3 21 4] Lo be the matrix for T: R2 → R² 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)]g where [v]p = [1 – 3]" c.) Find P-1 and A' (the matrix for T relative to B' d.) Find [T(v)]B, two ways.

1.) Let B {(1,1), (-2,3)}, and B' = {(1,-1), (0,1)} be bases for R?, and let A = | [3 21 4] Lo be the matrix for T: R2 → R² 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)]g where [v]p = [1 – 3]" c.) Find P-1 and A' (the matrix for T relative to B' d.) Find [T(v)]B, two ways.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.4: Transistion Matrices And Similarity

Problem 15E

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