Let B = {(1, 3), (-2,-2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let - [28] 24 be the matrix for T: R² → R² relative to B. A = (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [v] and [7(v)]B, where [v]B = [-3 5]T. [v] B = [T(V)]B (c) Find P-¹ and A' (the matrix for T relative to B'). p-1 = = A' = ↑ ↓↑ (d) Find [T(v)]B' two ways. [T(v)]B¹ = P¹[T(v)]B = [T(V)]B¹ = A'[V]B' = ← - ↓↑
Let B = {(1, 3), (-2,-2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let - [28] 24 be the matrix for T: R² → R² relative to B. A = (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [v] and [7(v)]B, where [v]B = [-3 5]T. [v] B = [T(V)]B (c) Find P-¹ and A' (the matrix for T relative to B'). p-1 = = A' = ↑ ↓↑ (d) Find [T(v)]B' two ways. [T(v)]B¹ = P¹[T(v)]B = [T(V)]B¹ = A'[V]B' = ← - ↓↑
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
Related questions
Question
![Let B = {(1, 3), (-2,-2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let
= [28]
24
be the matrix for T: R² → R² relative to B.
A =
(a) Find the transition matrix P from B' to B.
P =
(b) Use the matrices P and A to find [v] and [7(v)]B, where
[v]B = [-3 5]T.
[v] B =
[T(V)]B
(c) Find P-¹ and A' (the matrix for T relative to B').
33
p-1 =
=
A' =
↑
↓↑
(d) Find [T(v)]B' two ways.
[T(v)]B¹ = P¹[T(v)]B =
[T(v)]B¹ = A'[v]B¹
=
-
↓↑](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe2cc96c-bc7b-44cb-84d7-ccc50133ecf7%2F79fda27d-08c2-4480-88ad-975ca5f275c5%2Frn4zkau_processed.png&w=3840&q=75)
Transcribed Image Text:Let B = {(1, 3), (-2,-2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let
= [28]
24
be the matrix for T: R² → R² relative to B.
A =
(a) Find the transition matrix P from B' to B.
P =
(b) Use the matrices P and A to find [v] and [7(v)]B, where
[v]B = [-3 5]T.
[v] B =
[T(V)]B
(c) Find P-¹ and A' (the matrix for T relative to B').
33
p-1 =
=
A' =
↑
↓↑
(d) Find [T(v)]B' two ways.
[T(v)]B¹ = P¹[T(v)]B =
[T(v)]B¹ = A'[v]B¹
=
-
↓↑
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