Let Q(x) = 15x² − 2x² – 2x² + 12x1x2 + 12x1x3 – 8x2x3. Find a unit vector x in R³ whose first entry is positive at which Q(x) is minimized, subject to x¹x = 1. [Hint: The eigenvalues of the matrix of the quadratic form Q are 2, -9, and 18.] Enter the components of x (in order) into the answer box below, separated with commas.

Let Q(x) = 15x² − 2x² – 2x² + 12x1x2 + 12x1x3 – 8x2x3. Find a unit vector x in R³ whose first entry is positive at which Q(x) is minimized, subject to x¹x = 1. [Hint: The eigenvalues of the matrix of the quadratic form Q are 2, -9, and 18.] Enter the components of x (in order) into the answer box below, separated with commas.

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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