(c) (d) spaces What is the matrix of T with respect to the standard basis of both vector What is T(2 3
(c) (d) spaces What is the matrix of T with respect to the standard basis of both vector What is T(2 3
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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can you please answer c & d? Thank you
![1) Let T: R³ → M2×2 (R) be a linear map and suppose the dual map has matrix (with respect
to the standard basis of both vector spaces)
(b)
(c)
(d)
0
(a)
- (85) ₁ be the second standard basis vector in M2x2 (R). Write
T* (m) as a sum of the dual basis vectors in (R³)* (Hint: recall how matrices of linear
transformations are constructed: what are the columns?)
Using part a, what is (7*(m2)) (2)
What is the matrix of T with respect to the standard basis of both vector
spaces
Let m₂ =
[T*]
1
What is T(2)
3
=
1 2
01
8
1 0
-20
4 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb708fa5-116d-42c3-bb62-31dd00678e29%2Fd7d8250f-073c-48e1-8bec-024f758f3cf8%2F0yp89g8_processed.png&w=3840&q=75)
Transcribed Image Text:1) Let T: R³ → M2×2 (R) be a linear map and suppose the dual map has matrix (with respect
to the standard basis of both vector spaces)
(b)
(c)
(d)
0
(a)
- (85) ₁ be the second standard basis vector in M2x2 (R). Write
T* (m) as a sum of the dual basis vectors in (R³)* (Hint: recall how matrices of linear
transformations are constructed: what are the columns?)
Using part a, what is (7*(m2)) (2)
What is the matrix of T with respect to the standard basis of both vector
spaces
Let m₂ =
[T*]
1
What is T(2)
3
=
1 2
01
8
1 0
-20
4 0
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