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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
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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(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. :
Transcribed Image Text:(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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