F(x,y, z) = 5x² + 2y² + 4xy + xz
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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Transcribed Image Text:Consider the following quadratic form;
F(x, y, z) = 5x² + 2y² + 4xy + xz
Identify the symmetric coefficients matrix, A, associated with this
quadratic form. Find all principal sub-matrices of A and find all leading principal
a.
minors.
b.
Find the gradient vector at F(1, 0, 1) and interpret its meaning.
Define what it means for a quadratic form to be indefinite.
Determine the definiteness of this quadratic form.
C.
d.
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