Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R², and let20A =4 3be the matrix for T: R² → R² relative to B.(a) Find the transition matrix P from B' to B.P =188-↓ 1(b) Use the matrices P and A to find [v] and [7(v)]gr where[v] = [4 -1].[v] B =[T(V)] B =(c) Find P-¹ and A' (the matrix for T relative to B').p-1 =A'=

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Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R², and let 20 *- [39] A = 4 be the matrix for T: R² R² relative to B. (a) Find the transition matrix P from B' to B. P = 188 (b) Use the matrices P and A to find [v] and [T(v)] gr where [v] = [4 -1]. [v] B = [T(V)] B = ↓ 1

Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R², and let 20 *- [39] A = 4 be the matrix for T: R² R² relative to B. (a) Find the transition matrix P from B' to B. P = 188 (b) Use the matrices P and A to find [v] and [T(v)] gr where [v] = [4 -1]. [v] B = [T(V)] B = ↓ 1

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 13E

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Question

Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R², and let
20
A =
4 3
be the matrix for T: R² → R² relative to B.
(a) Find the transition matrix P from B' to B.
P =
188-
↓ 1
(b) Use the matrices P and A to find [v] and [7(v)]gr where
[v] = [4 -1].
[v] B =
[T(V)] B =
(c) Find P-¹ and A' (the matrix for T relative to B').
p-1 =
A'=

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