Find a 3 x 3 symmetric matrix M with eigenvalues A1 = 1 and A2 = 3 whosegeometric 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 beenable to find such an M? If we had replaced the eigenvalue A by 5, wouldyou have been able to find such an M?

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Answered: Find a 3 x 3 symmetric matrix M with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.