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6. Determine if the following quadratic forms are positive definite, positive semidefinite, negative definite, negative semidefinite, or indefinite. 4 (a) f(x) = x¹ [ = 0 2 (b) g(x) = x¹|–1 2 -2 -1 0 2 - 1 x 0 -1 2 (c) h(x₁, x2, x3) = x² + 2x²x₁x3

6. Determine if the following quadratic forms are positive definite, positive semidefinite, negative definite, negative semidefinite, or indefinite. 4 (a) f(x) = x¹ [ = 0 2 (b) g(x) = x¹|–1 2 -2 -1 0 2 - 1 x 0 -1 2 (c) h(x₁, x2, x3) = x² + 2x²x₁x3

Advanced Engineering Mathematics
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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6. Determine if the following quadratic forms are positive definite, positive semidefinite, negative definite, negative semidefinite, or indefinite. 2 -4 (a) f(x) = x¹ [-¹ 0 2 (b) g(x) = x¹ |–1 x -1 0 2 -1 X 0 -1 2 (c) h(x₁, x2, x3) = x² + 2x² − x₁x3
Transcribed Image Text:6. Determine if the following quadratic forms are positive definite, positive semidefinite, negative definite, negative semidefinite, or indefinite. 2 -4 (a) f(x) = x¹ [-¹ 0 2 (b) g(x) = x¹ |–1 x -1 0 2 -1 X 0 -1 2 (c) h(x₁, x2, x3) = x² + 2x² − x₁x3
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