(m) A represents the quadratic form q(x, y) = x² + 4xy + y²; for what values of (x, y) = R², q(x, y) = 0?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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part M urgntly need

(j) A = B+C, where B is an n x n symmetric positive-definite matrix and C is a singular
nx n symmetric matrix;
(k) A = B², where B is a symmetric negative-definite matrix;
(1) A = BCB, where C' is an n x n symmetric positive-definite and B is an nx n symmetric
negative-semidefinite matrix;
(m) A represents the quadratic form q(x, y) = x² + 4xy + y²; for what values of (x, y) = R²,
q(x, y) = 0?
Transcribed Image Text:(j) A = B+C, where B is an n x n symmetric positive-definite matrix and C is a singular nx n symmetric matrix; (k) A = B², where B is a symmetric negative-definite matrix; (1) A = BCB, where C' is an n x n symmetric positive-definite and B is an nx n symmetric negative-semidefinite matrix; (m) A represents the quadratic form q(x, y) = x² + 4xy + y²; for what values of (x, y) = R², q(x, y) = 0?
Determine whether the matrix A is positive-definite, negative-definite, positive-semidefinite,
negative-semidefinite,
indefinite, or zero matrix:
[5 17
(a) A =
2
(b) A =
(c) A=
(d) A = - [16
5 10]
10 2
(e) A =
10 2
(f) A represents the quadratic form q(x, y) = x² + 4xy + 4y²;
-5 107
(g) A =
10]:
; discuss your answer in dependence on the value of the parameter a € R;
10
5
10 √2
(h) A 10
2 α
√2 α B
; discuss your answer in dependence on the value of the parameters
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);
=
1
N
Transcribed Image Text:Determine whether the matrix A is positive-definite, negative-definite, positive-semidefinite, negative-semidefinite, indefinite, or zero matrix: [5 17 (a) A = 2 (b) A = (c) A= (d) A = - [16 5 10] 10 2 (e) A = 10 2 (f) A represents the quadratic form q(x, y) = x² + 4xy + 4y²; -5 107 (g) A = 10]: ; discuss your answer in dependence on the value of the parameter a € R; 10 5 10 √2 (h) A 10 2 α √2 α B ; discuss your answer in dependence on the value of the parameters 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); = 1 N
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