Let Q(x) = 21x² + 3x2 +21x3 +24x₁x₂ −12x₁ x3 +24X2X3. Find a unit vector x in R³ at which Q(x) is maximized, subject to xJx=1. [Hint: The eigenvalues of the matrix of the quadratic form Q are 27 and -9.]
Let Q(x) = 21x² + 3x2 +21x3 +24x₁x₂ −12x₁ x3 +24X2X3. Find a unit vector x in R³ at which Q(x) is maximized, subject to xJx=1. [Hint: The eigenvalues of the matrix of the quadratic form Q are 27 and -9.]
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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Let Q(x) = 21x² + 3x2 +21x3 +24x₁x₂ - 12x₁ x3 +24x2x3. Find a unit vector x in R3 at which Q(x) is maximized, subject to
T
x'x= 1.
[Hint: The eigenvalues of the matrix of the quadratic form Q are 27 and -9.]
A unit vector that maximizes Q(x) is u =
(Type an exact answer, using radicals as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9a65136-19b0-4d4f-9639-5a5599fc2b90%2Fbf88dc35-358a-4641-9c14-45bb2c87e240%2F5xeadft_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Vo
nt
Let Q(x) = 21x² + 3x2 +21x3 +24x₁x₂ - 12x₁ x3 +24x2x3. Find a unit vector x in R3 at which Q(x) is maximized, subject to
T
x'x= 1.
[Hint: The eigenvalues of the matrix of the quadratic form Q are 27 and -9.]
A unit vector that maximizes Q(x) is u =
(Type an exact answer, using radicals as needed.)
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