1. Compute (a) the characteristic polynomial of A, (b) the eigenvalues of A, (c) a basis for eacheigenspace of A, and (d) the algebraic and geometric multiplicity of each eigenvalue.1201A =|-1-1111.2. A is a 3 × 3 matrix with eigenvectors vị = |0|,v2 =,V3 =corresponding to eigenvalues21 = -12 =z = 1, respectively, and x = |1|. Find A2ºx.

Eigenvalues and Eigenvectors of the matrix

1. Compute (a) the characteristic polynomial of A, (b) the eigenvalues of A, (c) a basis for each eigenspace of A, and (d) the algebraic and geometric multiplicity of each eigenvalue. 2 01 A -1 -1 1 0 1 = [0], v₂ = [1], v₁ = [1] corresponding to eigenvalues 2. A is a 3 x 3 matrix with eigenvectors v₁ = 0,0₂ V3

1. Compute (a) the characteristic polynomial of A, (b) the eigenvalues of A, (c) a basis for each eigenspace of A, and (d) the algebraic and geometric multiplicity of each eigenvalue. 2 01 A -1 -1 1 0 1 = [0], v₂ = [1], v₁ = [1] corresponding to eigenvalues 2. A is a 3 x 3 matrix with eigenvectors v₁ = 0,0₂ V3

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 12EQ

See similar textbooks