For each matrix A below, find eigenvalues for the induced linear operator T on F^n without performing any calculations. Then describe the eigenvectors v in F^n associated to each eigenvalue lambda by looking at solutions to the matrix equation (A - lambda*I)v = 0 where I denotes the identity map on F^n. (a) row 1: -1, 6 ; row 2: 0, 5. (b) row 1: -1/3, 0, 0, 0 ; row 2: 0, -1/3, 0, 0 ; row 3: 0, 0, 1, 0 ; row 4: 0, 0, 0, 1/2. (c) row 1: 1, 3, 7, 11 ; row 2: 0, 1/2, 3, 8 ; row 3: 0, 0, 0, 4 ; row 4: 0, 0, 0, 2.

For each matrix A below, find eigenvalues for the induced linear operator T on F^n without performing any calculations. Then describe the eigenvectors v in F^n associated to each eigenvalue lambda by looking at solutions to the matrix equation (A - lambda*I)v = 0 where I denotes the identity map on F^n. (a) row 1: -1, 6 ; row 2: 0, 5. (b) row 1: -1/3, 0, 0, 0 ; row 2: 0, -1/3, 0, 0 ; row 3: 0, 0, 1, 0 ; row 4: 0, 0, 0, 1/2. (c) row 1: 1, 3, 7, 11 ; row 2: 0, 1/2, 3, 8 ; row 3: 0, 0, 0, 4 ; row 4: 0, 0, 0, 2.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 10AEXP

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