[10 010 0 2 1 000 2 Answer the questions below for the matrix A = 0 (a) Find all eigenvalues of A. (b) For each eigenvalue A₁, we define the eigenspace Ex₂ = null (A - X; I) to be the nullspace of A-XI. For each eigenvalue A₁, use the rank-nullity theorem to calculate dim(Ex) and find a basis for Ex. Recall that the rank-nullity theorem says that, for an m by n matrix T, rank(T) + nullity(T) = n. (c) Is A diagonalizable? Explain.

[10 010 0 2 1 000 2 Answer the questions below for the matrix A = 0 (a) Find all eigenvalues of A. (b) For each eigenvalue A₁, we define the eigenspace Ex₂ = null (A - X; I) to be the nullspace of A-XI. For each eigenvalue A₁, use the rank-nullity theorem to calculate dim(Ex) and find a basis for Ex. Recall that the rank-nullity theorem says that, for an m by n matrix T, rank(T) + nullity(T) = n. (c) Is A diagonalizable? Explain.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...

See similar textbooks