Problem 1 (Diagonalisation)Let5 -4 2A==-- (1:0)=-2 2-3 2 ER³X3a) Show that \and determine a basis for the corresponding eigenspace.-1 is an eigenvalue of A with geometric multiplicity 2,b) Show that v :=(3)2 is an eigenvector of A,and calculate the associated eigenvalue.c) Show that A is diagonalisable and find an invertible matrix X E R³×3 and a diagonal matrix Dsuch that X-¹AX = D.d) Find a 3 x 3-matrix B such that B2 = A.

Answered: Image /qna-images/answer/ae18e885-5cc3-4cb1-9a1a-041affb98105.jpg

Problem 1 (Diagonalisation) Let A == 5 -4 2 4 -2 2 0 -3 2 € R3x3 a) Show that λ = 1 is an eigenvalue of A with geometric multiplicity 2, and determine a basis for the corresponding eigenspace. 2 b) Show that v := 2 is an eigenvector of A, and calculate the associated eigenvalue. c) Show that A is diagonalisable and find an invertible matrix X E R3x3 and a diagonal matrix D such that X-¹AX = D.

Problem 1 (Diagonalisation) Let A == 5 -4 2 4 -2 2 0 -3 2 € R3x3 a) Show that λ = 1 is an eigenvalue of A with geometric multiplicity 2, and determine a basis for the corresponding eigenspace. 2 b) Show that v := 2 is an eigenvector of A, and calculate the associated eigenvalue. c) Show that A is diagonalisable and find an invertible matrix X E R3x3 and a diagonal matrix D such that X-¹AX = D.

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 41EQ

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