Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject to the constraint. w = 6x² - 3y² = 32² + 12xy = 12xz + 24yz; x² + y² + z² = 1 The constrained maximum of constrained minimum of occurs at two sets of coordinates. The set of coordinates with the smaller x value is (x, y, z) = occurs when (x, y, z)= | and the set of coordinates with the larger x value is (x, y, z)= The
Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject to the constraint. w = 6x² - 3y² = 32² + 12xy = 12xz + 24yz; x² + y² + z² = 1 The constrained maximum of constrained minimum of occurs at two sets of coordinates. The set of coordinates with the smaller x value is (x, y, z) = occurs when (x, y, z)= | and the set of coordinates with the larger x value is (x, y, z)= The
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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![**Problem Statement:**
Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject to the constraint.
\[ w = 6x^2 - 3y^2 - 3z^2 + 12xy - 12xz + 24yz; \quad x^2 + y^2 + z^2 = 1 \]
**Solutions:**
The constrained maximum of \(\_\_\_\_\_\_\) occurs at two sets of coordinates. The set of coordinates with the smaller \(x\) value is \((x, y, z) = (\_\_\_\_\_\_, \_\_\_\_\_\_, \_\_\_\_\_\_)\), and the set of coordinates with the larger \(x\) value is \((x, y, z) = (\_\_\_\_\_\_, \_\_\_\_\_\_, \_\_\_\_\_\_)\).
The constrained minimum of \(\_\_\_\_\_\_\) occurs when \((x, y, z) = (\_\_\_\_\_\_, \_\_\_\_\_\_, \_\_\_\_\_\_)\).
**Note:** Replace blanks with the correct values once calculated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ff295b-afd4-43c3-8ed2-2cc17b9c2249%2F10ef27e0-6013-4e59-b3de-02e21ec00eb8%2Fcz5e2g_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject to the constraint.
\[ w = 6x^2 - 3y^2 - 3z^2 + 12xy - 12xz + 24yz; \quad x^2 + y^2 + z^2 = 1 \]
**Solutions:**
The constrained maximum of \(\_\_\_\_\_\_\) occurs at two sets of coordinates. The set of coordinates with the smaller \(x\) value is \((x, y, z) = (\_\_\_\_\_\_, \_\_\_\_\_\_, \_\_\_\_\_\_)\), and the set of coordinates with the larger \(x\) value is \((x, y, z) = (\_\_\_\_\_\_, \_\_\_\_\_\_, \_\_\_\_\_\_)\).
The constrained minimum of \(\_\_\_\_\_\_\) occurs when \((x, y, z) = (\_\_\_\_\_\_, \_\_\_\_\_\_, \_\_\_\_\_\_)\).
**Note:** Replace blanks with the correct values once calculated.
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