Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A-[28] = 40 be the matrix for T: R2 R2 relative to B. → (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [v] and [T(v)]B, where [v]B = [-5 4]. [V]B [T(v)]B 11 = p-1 = 11 (c) Find P-1 and A' (the matrix for T relative to B'). 11

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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(c) Find P-1 and A' (the matrix for T relative to B').
p-1 =
A' =
11
(d) Find [T(v)]B' two ways.
[T(v)]B = P-¹[T(v)]B
[T(v)]B' = A'[v]B'
=
1
11
11
Transcribed Image Text:(c) Find P-1 and A' (the matrix for T relative to B'). p-1 = A' = 11 (d) Find [T(v)]B' two ways. [T(v)]B = P-¹[T(v)]B [T(v)]B' = A'[v]B' = 1 11 11
Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let
3 2
40
be the matrix for T: R2 R2 relative to B.
56°F
A =
(a) Find the transition matrix P from B' to B.
P =
(b) Use the matrices P and A to find [v] and [T(v)]B, where
[v]B = [-5 4]T.
[V] B
[T(v)]B
=
(c) Find P-1 and A' (the matrix for T relative to B').
p-1 =
4
Transcribed Image Text:Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let 3 2 40 be the matrix for T: R2 R2 relative to B. 56°F A = (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [v] and [T(v)]B, where [v]B = [-5 4]T. [V] B [T(v)]B = (c) Find P-1 and A' (the matrix for T relative to B'). p-1 = 4
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