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.
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) = 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe60e14a8-856f-447c-ac90-795ae43e00b4%2Fa319bd7d-8d0b-4c63-8bd0-8799f36025fb%2Frgkxtdh_processed.png&w=3840&q=75)
Transcribed Image Text: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.
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