Exercise 2 (Quadratic forms II). Prove that for a symmetric quadratic form Q(x1,x2) with associated matrix A = holds (i) Q(x1,x2) is negative definite iff a11 <0 and a11a22 - a² 12 > 0; (ii) Q(x1,x2) is negative semidefinite iff α11 ≤ 0,022 ≤ 0 and a11a22 - a 12 ≥ 0. (aij)2 it

Exercise 2 (Quadratic forms II). Prove that for a symmetric quadratic form Q(x1,x2) with associated matrix A = holds (i) Q(x1,x2) is negative definite iff a11 <0 and a11a22 - a² 12 > 0; (ii) Q(x1,x2) is negative semidefinite iff α11 ≤ 0,022 ≤ 0 and a11a22 - a 12 ≥ 0. (aij)2 it

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 43E

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Exercise 2 (Quadratic forms II).
Prove that for a symmetric quadratic form Q(x1,x2) with associated matrix A =
holds
(i) Q(x1,x2) is negative definite iff a11 <0 and a11a22 - a² 12 > 0;
(ii) Q(x1,x2) is negative semidefinite iff α11 ≤ 0,022 ≤ 0 and a11a22 - a 12 ≥ 0.
(aij)2 it

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