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0 0 51 Let C =0 3 0 l2 0 ol 1. Is C diagonal? If no, diagonalize C using the spectral theorem of linear algebra. 2. Base on (a), determine the signature, spectrum, and inertia of C. 3. Obtain the quadratic form q(x), where x [x x2 x3]". What can be said about its definiteness?

0 0 51 Let C =0 3 0 l2 0 ol 1. Is C diagonal? If no, diagonalize C using the spectral theorem of linear algebra. 2. Base on (a), determine the signature, spectrum, and inertia of C. 3. Obtain the quadratic form q(x), where x [x x2 x3]". What can be said about its definiteness?

Advanced Engineering Mathematics
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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[o 0 5 Let C = 0 3 0 l2 o ol 1. Is C diagonal? If no, diagonalize C using the spectral theorem of linear algebra. 2. Base on (a), determine the signature, spectrum, and inertia of C. 3. Obtain the quadratic form q(x), where x = [x x2 x3]". What can be said about its definiteness? 4. If b = [1 -1 o]", determine whether the matrix equation Ax = b indicates a solution by constructing its augmented matrix. Is there is a solution? Is the solution unique? If yes, obtain x' using Cramer's rule.
Transcribed Image Text:[o 0 5 Let C = 0 3 0 l2 o ol 1. Is C diagonal? If no, diagonalize C using the spectral theorem of linear algebra. 2. Base on (a), determine the signature, spectrum, and inertia of C. 3. Obtain the quadratic form q(x), where x = [x x2 x3]". What can be said about its definiteness? 4. If b = [1 -1 o]", determine whether the matrix equation Ax = b indicates a solution by constructing its augmented matrix. Is there is a solution? Is the solution unique? If yes, obtain x' using Cramer's rule.
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