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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![(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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcef0b9a8-6e5a-4ac8-9e4d-236d7fc541c9%2Fc6a4ec68-2bd1-4d8e-84ba-3cfa83f4429e%2F84giyeb_processed.jpeg&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcef0b9a8-6e5a-4ac8-9e4d-236d7fc541c9%2Fc6a4ec68-2bd1-4d8e-84ba-3cfa83f4429e%2Fzq6ixml_processed.jpeg&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
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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