Let Q(x) = - 6x, + 2x5 + 8x1X2 - 8x2X3. Find a unit vector x in R' at which Q(x) is maximized, subject to x'x= 1. [Hint: The eigenvalues of the matrix of the quadratic form Q are 6, - 2, - 8.] A unit vector that maximizes Q(x) is u = (Type an exact answer, using radicals as needed.)

Let Q(x) = - 6x, + 2x5 + 8x1X2 - 8x2X3. Find a unit vector x in R' at which Q(x) is maximized, subject to x'x= 1. [Hint: The eigenvalues of the matrix of the quadratic form Q are 6, - 2, - 8.] A unit vector that maximizes Q(x) is u = (Type an exact answer, using radicals as needed.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.6: The Algebra Of Matrices

Problem 13E

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Question

Let Q(x) = - 6x + 2x3 + 8x,x2 - 8x2X3. Find a unit vector x in R at which Q(x) is maximized, subject to x'x= 1.
[Hint: The eigenvalues of the matrix of the quadratic form Q are 6, - 2, - 8.]
A unit vector that maximizes Q(x) is u =
(Type an exact answer, using radicals as needed.)

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