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(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
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
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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