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Find a 3 x 3 symmetric matrix M with eigenvalues A1 = 1 and X2 = 3 whose geometric multiplicities are 2 and 1 respectively, such that: %3D 1. (1, –1, 1)', (2, 0, 1)' are eigenvectors for 2. 2. (–1,1,2)' is an eigenvector for 3.

Find a 3 x 3 symmetric matrix M with eigenvalues A1 = 1 and X2 = 3 whose geometric multiplicities are 2 and 1 respectively, such that: %3D 1. (1, –1, 1)', (2, 0, 1)' are eigenvectors for 2. 2. (–1,1,2)' is an eigenvector for 3.

Linear Algebra: A Modern Introduction
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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Find a 3 x 3 symmetric matrix M with eigenvalues A1 = 1 and A2 = 3 whose geometric multiplicities are 2 and 1 respectively, such that: 1. (1, –1,1)*, (2, 0, 1)' are eigenvectors for 2. 2. (–1,1,2)' is an eigenvector for 3. If we had replaced (-1, 1,2)' in item (2) by (–1, 1, 1)', would you have been able to find such an M? If we had replaced the eigenvalue A by 5, would you have been able to find such an M?
Transcribed Image Text:Find a 3 x 3 symmetric matrix M with eigenvalues A1 = 1 and A2 = 3 whose geometric multiplicities are 2 and 1 respectively, such that: 1. (1, –1,1)*, (2, 0, 1)' are eigenvectors for 2. 2. (–1,1,2)' is an eigenvector for 3. If we had replaced (-1, 1,2)' in item (2) by (–1, 1, 1)', would you have been able to find such an M? If we had replaced the eigenvalue A by 5, would you have been able to find such an M?
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