Consider the following bases B and B' for some subspace of M2x2 (R), the vector space of all 2 by 2 matrices over R. 10 3 3 B' = B-{[13]- [23] [21]}- - -{[82] [83] [24]} = 2 히 relative to the basis B', that is [ 2 (a) Find the coordinate matrix of A = [x(A)] Br. (b) Calculate the transition matrix PB'→B. [Show steps.] (c) Use part 2(b) to calculate the coordinate matrix of A relative to the basis B. (d) Verify the coordinate matrix obtained in part 2(c).
Consider the following bases B and B' for some subspace of M2x2 (R), the vector space of all 2 by 2 matrices over R. 10 3 3 B' = B-{[13]- [23] [21]}- - -{[82] [83] [24]} = 2 히 relative to the basis B', that is [ 2 (a) Find the coordinate matrix of A = [x(A)] Br. (b) Calculate the transition matrix PB'→B. [Show steps.] (c) Use part 2(b) to calculate the coordinate matrix of A relative to the basis B. (d) Verify the coordinate matrix obtained in part 2(c).
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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![Consider the following bases B and B' for some subspace of M2x2(R), the vector space
of all 2 by 2 matrices over R.
n-{[: :] [:}] [::}
- {[i '].
0 0
3 4
1 0
1 1
3 1
3 0
3
B =
B' =
2 3
3
2
-8
-6 -1
(a) Find the coordinate matrix of A
relative to the basis B', that is
[x(A)]g"-
(b) Calculate the transition matrix Pg¬B- [Show steps.]
(c) Use part 2(b) to calculate the coordinate matrix of A relative to the basis B.
(d) Verify the coordinate matrix obtained in part 2(c).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2b5459d-4e11-4c8b-b192-abec4422f7ae%2F458aa398-8dca-4915-bc8f-80fabe4185bc%2Fd4bec0d_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following bases B and B' for some subspace of M2x2(R), the vector space
of all 2 by 2 matrices over R.
n-{[: :] [:}] [::}
- {[i '].
0 0
3 4
1 0
1 1
3 1
3 0
3
B =
B' =
2 3
3
2
-8
-6 -1
(a) Find the coordinate matrix of A
relative to the basis B', that is
[x(A)]g"-
(b) Calculate the transition matrix Pg¬B- [Show steps.]
(c) Use part 2(b) to calculate the coordinate matrix of A relative to the basis B.
(d) Verify the coordinate matrix obtained in part 2(c).
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