Consider the following matrix1 0 0 02 2 0 0[A] =1 0 3 00 1 k 4a) In order for [2corresponding to this eigenvector.-4-1 1E to be an eigenvector of [A], detemine the value of k, and the eigenvalueb) Calculate trace[A]c) By setting k to -1 in [A], another matrix [B]is formed:[1 02 2[B] =1 030 1 -1 4By using properties of eigenvalues, determine all the eigenvalues of the matrix and explain. (Do not makeany computations).

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[1 0 0 0 2 2 0 0 1 03 0 0 1 k 4 [A] = a) In order for [2 4 -1 1E to be an eigenvector of [A], detemine the value of k, and the eigenvalue corresponding to this eigenvector. b) Calculate trace[A] c) By setting k to -1 in [A], another matrix [B] is formed: [1 0 0 0 2 2 [B] = 1 0 3 0 1 -1 4 By using properties of eigenvalues, detemine all the eigenvalues of the matrix and explain. (Do not make any computations).

[1 0 0 0 2 2 0 0 1 03 0 0 1 k 4 [A] = a) In order for [2 4 -1 1E to be an eigenvector of [A], detemine the value of k, and the eigenvalue corresponding to this eigenvector. b) Calculate trace[A] c) By setting k to -1 in [A], another matrix [B] is formed: [1 0 0 0 2 2 [B] = 1 0 3 0 1 -1 4 By using properties of eigenvalues, detemine all the eigenvalues of the matrix and explain. (Do not make any computations).

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...

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