. Let B = {(1,–1),(-2,1) } and B' = {(-1,1), (1,2) } be basis for R² , and let A = 6 I be the matrix for T:R2 → R2 relative to B. Given transition matrix from B' to B to be P = Use the graph below to answer the following questions. V (Basis B) [v]g [T(v)]g p- (Basis B') [v]g [T(v)]g V V a. Use the matrices P and A to find [v]B and [T(v)].,, where [V]B, = [1 -4]T. b. Find P-1 and the matrix A' for T relative to B'. c. Use A' to Find [T(v)|R; BI
. Let B = {(1,–1),(-2,1) } and B' = {(-1,1), (1,2) } be basis for R² , and let A = 6 I be the matrix for T:R2 → R2 relative to B. Given transition matrix from B' to B to be P = Use the graph below to answer the following questions. V (Basis B) [v]g [T(v)]g p- (Basis B') [v]g [T(v)]g V V a. Use the matrices P and A to find [v]B and [T(v)].,, where [V]B, = [1 -4]T. b. Find P-1 and the matrix A' for T relative to B'. c. Use A' to Find [T(v)|R; BI
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,–1).(-2,1) } and B' = {(-1,1), (1,2) } be basis for
R2, and let A
2
be the matrix for T:R2 → R² relative to
0]
B. Given transition matrix from B' to B to be P
|
1
Use
|
the graph below to answer the following questions.
V
V
(Basis B)
[v]B
A
(T(v)]B
(Basis B')
[v]g
A'
(T(v)lg
V
a. Use the matrices P and A to find [v]B and |T(v).,, where
[v]B, = [1 -4]".
b. Find P-1 and the matrix A' for T relative to B'.
c. Use A' to Find [T(v)R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabc5aa9d-951a-40e1-86a3-f092042c4046%2F88253ee5-cd0c-427d-8a36-a11cfec3b90f%2Fikmcvpm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:. Let B = {(1,–1).(-2,1) } and B' = {(-1,1), (1,2) } be basis for
R2, and let A
2
be the matrix for T:R2 → R² relative to
0]
B. Given transition matrix from B' to B to be P
|
1
Use
|
the graph below to answer the following questions.
V
V
(Basis B)
[v]B
A
(T(v)]B
(Basis B')
[v]g
A'
(T(v)lg
V
a. Use the matrices P and A to find [v]B and |T(v).,, where
[v]B, = [1 -4]".
b. Find P-1 and the matrix A' for T relative to B'.
c. Use A' to Find [T(v)R
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