Question 22.1. Consider the general case of a quadratic form in R2,а bQ(x1, 22) = [ ¤1 r2]b.which is subject to the linear constraint Ax +X2Bx2 = 0. Show that Q is positive definite on the constraint set if and only if aB²26AB + cA? > 0 and negative definite if and only if aB2 - 26AB + cA? < 0.

Name: Question 22.1. Consider the general case of a quadratic form in R2,а
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Description: Question 22.1. Consider the general case of a quadratic form in R2,а bQ(x1, 22) = [ ¤1 r2]b.which is subject to the linear constraint Ax +X2Bx2 = 0. Show that Q is positive definite on the constraint set if and only if aB²26AB + cA? > 0 and negative

A quadratic form will be positive (negative) definite if it is always positive (negative) for all…

Math

Advanced Math

Question 2 2.1. Consider the general case of a quadratic form in R, a b Q(x1, x2) = [ ¤1 x2] which is subject to the linear constraint Ax, + 6 c Bx2 = 0. Show that Q is positive definite on the constraint set if and only if aB2 26AB + cA? > 0 and negative definite if and only if aB2 - 26AB + cA? < 0.

Question 2 2.1. Consider the general case of a quadratic form in R, a b Q(x1, x2) = [ ¤1 x2] which is subject to the linear constraint Ax, + 6 c Bx2 = 0. Show that Q is positive definite on the constraint set if and only if aB2 26AB + cA? > 0 and negative definite if and only if aB2 - 26AB + cA? < 0.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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