(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
icon
Related questions
Question

part D E F

(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
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,