Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4, 4)} be bases for R2, and let 23 04 A = be the matrix for T: R² R2 relative to B. (a) Find the transition matrix P from B' to B. P = 6 [V] B (b) Use the matrices P and A to find [v] and [T(v)]B, where [v] B = [-4 3]T. [T(V)] B 4 11 -12 -1/3 4 -24 -96 JE = -96 11 - (c) Find P-1 and A' (the matrix for T relative to B'). 1/3 1
Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4, 4)} be bases for R2, and let 23 04 A = be the matrix for T: R² R2 relative to B. (a) Find the transition matrix P from B' to B. P = 6 [V] B (b) Use the matrices P and A to find [v] and [T(v)]B, where [v] B = [-4 3]T. [T(V)] B 4 11 -12 -1/3 4 -24 -96 JE = -96 11 - (c) Find P-1 and A' (the matrix for T relative to B'). 1/3 1
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
![Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4, 4)} be bases for R², and let
23
= [33]
04
A =
R2 relative to B.
(a) Find the transition matrix P from B' to B.
be the matrix for T: R² ->>>
P =
6
9
[V] B
[T(V)]B =
(b) Use the matrices P and A to find [v] and [T(v)]B, where
[V] B¹ = [-4 3].
-12
-1/3
-24
-96
4
-96
4
11
←
(c) Find P-1 and A' (the matrix for T relative to B').
1/3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe23422ac-9509-4709-8628-5f27bfc79429%2Fc9791ba5-202a-4639-bc4f-0ca4de903537%2Fw1l3za3j_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
23
= [33]
04
A =
R2 relative to B.
(a) Find the transition matrix P from B' to B.
be the matrix for T: R² ->>>
P =
6
9
[V] B
[T(V)]B =
(b) Use the matrices P and A to find [v] and [T(v)]B, where
[V] B¹ = [-4 3].
-12
-1/3
-24
-96
4
-96
4
11
←
(c) Find P-1 and A' (the matrix for T relative to B').
1/3
![(c) Find P-1 and A' (the matrix for T relative to B').
p-1 =
A' =
-1/3
3/4
-1
45/4
1/3
-1/2
-4/3
7
(d) Find [T(v)]B two ways.
[T(v)]B = P¹[T(v)]B
[T(v)]B = A'[v]B'
=
=
X
-258
-136
11
→](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe23422ac-9509-4709-8628-5f27bfc79429%2Fc9791ba5-202a-4639-bc4f-0ca4de903537%2Fig36bz_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' =
-1/3
3/4
-1
45/4
1/3
-1/2
-4/3
7
(d) Find [T(v)]B two ways.
[T(v)]B = P¹[T(v)]B
[T(v)]B = A'[v]B'
=
=
X
-258
-136
11
→
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