Let A be a 3 x 3 matrix: A = a11 a12 a13 a21 a22 a23 a31 a32 a33 The entries a, 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 a, 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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