(d) A= 5 10 10 2 ; -5 (e) A = 20]; 10 2 (f) A represents the quadratic form q(x, y) = x² + 4xy + 4y²;
(d) A= 5 10 10 2 ; -5 (e) A = 20]; 10 2 (f) A represents the quadratic form q(x, y) = x² + 4xy + 4y²;
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
part D E F
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64e9aeab-eb13-4ff5-9c6d-afbd36418e3b%2F0c9ea921-4e9e-4ed6-9582-8fa4c0960905%2Fb1f0lo_processed.jpeg&w=3840&q=75)
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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