Let A be a 3 x 3 matrix: A = a11 a12 a13 a21 a22 a23 a31 a32 a33 The entries aij, i, j = 1, 2, 3 are numbers. Let A be an eigenvalue of A. For i, j = 1, 2, 3, denote by Mij the (i, j)-minor of A-XI, where I is the 3 x 3 identity matrix. Show that the following vector -det (M21) det (M22) -det (M23) is an eigenvector of A with eigenvalue A. Show your work in details.

Let A be a 3 x 3 matrix: A = a11 a12 a13 a21 a22 a23 a31 a32 a33 The entries aij, i, j = 1, 2, 3 are numbers. Let A be an eigenvalue of A. For i, j = 1, 2, 3, denote by Mij the (i, j)-minor of A-XI, where I is the 3 x 3 identity matrix. Show that the following vector -det (M21) det (M22) -det (M23) is an eigenvector of A with eigenvalue A. Show your work in details.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 26EQ

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