Determine whether the matrix A is positive-definite, negative-definite, positive-semidefinite, negative-semidefinite, indefinite, or zero matrix: (a) A = [1]. -5 (b) A 5 (c) A = [74] (d) A = - [56 5 10] 10 2 5 (c) 4- [102]: A = (f) A represents the quadratic form q(x, y) = x² + 4xy + 4y²; -5 10 (g) A = ; discuss your answer in dependence on the value of the parameter a € R; 10 5 10 √2 (h) A = 10 2 a discuss your answer in dependence on the value of the parameters √2 a B a, BER; (i) A = B + C, where B and C are n x n symmetric positive-definite matrices (prove your claim, or demonstrate by examples why the provided information is not enough tot classify the type of matrix A); = 51 12
Determine whether the matrix A is positive-definite, negative-definite, positive-semidefinite, negative-semidefinite, indefinite, or zero matrix: (a) A = [1]. -5 (b) A 5 (c) A = [74] (d) A = - [56 5 10] 10 2 5 (c) 4- [102]: A = (f) A represents the quadratic form q(x, y) = x² + 4xy + 4y²; -5 10 (g) A = ; discuss your answer in dependence on the value of the parameter a € R; 10 5 10 √2 (h) A = 10 2 a discuss your answer in dependence on the value of the parameters √2 a B a, BER; (i) A = B + C, where B and C are n x n symmetric positive-definite matrices (prove your claim, or demonstrate by examples why the provided information is not enough tot classify the type of matrix A); = 51 12
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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