Let T be the linear operator on R 2 defined by T(x, y) = (−y, x) i. What is the matrix of T in the standard ordered basis for R 2 ? ii. What is the matrix of T in the ordered basis B = {α1, α2 }, where α1 = (1, 2) and α2 = (1, −1)? iii. Prove that for every real number c the operator (T − cI) is invertible.

Let T be the linear operator on R 2 defined by T(x, y) = (−y, x) i. What is the matrix of T in the standard ordered basis for R 2 ? ii. What is the matrix of T in the ordered basis B = {α1, α2 }, where α1 = (1, 2) and α2 = (1, −1)? iii. Prove that for every real number c the operator (T − cI) is invertible.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.5: Applications

Problem 30EQ

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