(a) Determine the definiteness of the following quadratic forms:q = - 41,7, + 2r,7, – – 4z + 6z,7,(ii) q = 2n – 3z + 5a? – 8x,7,(1)(b) Given the following matrix:1 0 0D = 0 3 00 0 2Find the eigenvalues and the eigenvectors of D.:

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(a) Determine the definiteness of the following quadratic forms: q = z - 4z,1, + 2x,x, – a – 4x; + 6z,7, (ii) q = 2r - 32 + 5x – 8z,7, (i) (b) Given the following matrix: (1 0 0 D =0 3 0 0 0 2 Find the eigenvalues and the eigenvectors of D.

(a) Determine the definiteness of the following quadratic forms: q = z - 4z,1, + 2x,x, – a – 4x; + 6z,7, (ii) q = 2r - 32 + 5x – 8z,7, (i) (b) Given the following matrix: (1 0 0 D =0 3 0 0 0 2 Find the eigenvalues and the eigenvectors of D.

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) Determine the definiteness of the following quadratic forms:
q = - 41,7, + 2r,7, – – 4z + 6z,7,
(ii) q = 2n – 3z + 5a? – 8x,7,
(1)
(b) Given the following matrix:
1 0 0
D = 0 3 0
0 0 2
Find the eigenvalues and the eigenvectors of D.
:

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