part L M urgntly needed 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 = - [165 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;10510 √2(h) A 102 α√2 α B; discuss your answer in dependence on the value of the parametersa, BER;(i) A = B + C, where B and C are n x n symmetric positive-definite matrices (proveyour claim, or demonstrate by examples why the provided information is not enough totclassify the type of matrix A);=1N (j) A = B+C, where B is an n x n symmetric positive-definite matrix and C is a singularnx 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 symmetricnegative-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?

In part l, We are given that A=BCB Here, C is n×n symmetric positive-definite. So, xTCx>0 with…

Answered: (1) A= BCB, where C is an n x n…

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(1) A= BCB, where C is an n x n symmetric positive-definite and B is an n x n symmetric matrix; negative-semidefinite

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 41EQ: In general, it is difficult to show that two matrices are similar. However, if two similar matrices...

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Question

part L M urgntly needed

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

(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?

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