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) spaces [T*] Let m₂ = = 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 1 2 01 8 1 0 -20 4 0

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) spaces [T] Let m₂ = = 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 1 2 01 8 1 0 -20 4 0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 23EQ

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