a) For the matrix M below, find the eigenvalues, the eigenvectors, a basis B of R³ for which the matrix [LM]B is diagonal and the change of basis matrix from the standard basis S = {e1,e2, e3} of R³ to B. Verify that (s AB)-1.M.s Ag is diagonal. 2. 2 M = -2 4 5 -1 [ -4 b) For which values of x E R does the matrix B = 2 have real eigenvalues? -2 c) Take x = +1 and find the eigenvectors of B.

a) For the matrix M below, find the eigenvalues, the eigenvectors, a basis B of R³ for which the matrix [LM]B is diagonal and the change of basis matrix from the standard basis S = {e1,e2, e3} of R³ to B. Verify that (s AB)-1.M.s Ag is diagonal. 2. 2 M = -2 4 5 -1 [ -4 b) For which values of x E R does the matrix B = 2 have real eigenvalues? -2 c) Take x = +1 and find the eigenvectors of B.

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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Question

a) For the matrix M below, find the eigenvalues, the eigenvectors, a basis B of R3 for which the
matrix [LM]B is diagonal and the change of basis matrix from the standard basis S = {e1,e2, e3}
of R³ to B. Verify that (s AB)-!.M.s Ag is diagonal.
2
M =
-2
4
-1
-4
b) For which values of x ER does the matrix B =
have real eigenvalues?
-2
c) Take x = +1 and find the eigenvectors of B.
2.

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