(a) q = x² + 2xz + 2y² + 2yz + 2z² (b) q = x² + 2xz+ 2yz
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:Working over R, which of the following quadratic forms in 3 variables is positive definite (this is equivalent to s = 3, t = 0 in Sylvester's law of inertia for a 3 x 3
matrix).
(a) q= x² + 2xz+ 2y² + 2yz + 2z²
(b) q = x² + 2xz+ 2yz
Select one:
(b) and not (a)
O
The answer depends on the values of x, y, z
O
Both
Neither
O (a) and not (b)
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