[1 2 3 4 5 2 4 6 8 10 2. Let A= 3 6 9 12 15 4 8 12 16 20 5 10 15 20 25 (a) Find a vector v such that A = vv and show that v is an eigenvector of A. (b) Find the dimension of the nullspace of A. (c) Find all eigenvalues and their geometric multiplicities. (Hint: the nullspace of A is the 0-eigenspace of A.) (d) Diagonalize A, that is, find an invertible matrix X such that X-¹AX is a diagonal matrix.

[1 2 3 4 5 2 4 6 8 10 2. Let A= 3 6 9 12 15 4 8 12 16 20 5 10 15 20 25 (a) Find a vector v such that A = vv and show that v is an eigenvector of A. (b) Find the dimension of the nullspace of A. (c) Find all eigenvalues and their geometric multiplicities. (Hint: the nullspace of A is the 0-eigenspace of A.) (d) Diagonalize A, that is, find an invertible matrix X such that X-¹AX is a diagonal matrix.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section: Chapter Questions

Problem 9RQ

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