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Quadratic forms are given below. 1. V(x) = x,² + xz² + 3x3² – 2x1x2 2. V(x) = 5x,² + 2x2² + 3x3² + 2x,x2 3. V(x) = -4x,² – 2x,² – x3² + 4x,x2 4. V(x) = -x,² – 4x,² – x3² + 4x2X3 %3D Please identify are these functions positive semi-definite, negative semi-definite, positive definite, negative definite or non-definite in the R' space?

Quadratic forms are given below. 1. V(x) = x,² + xz² + 3x3² – 2x1x2 2. V(x) = 5x,² + 2x2² + 3x3² + 2x,x2 3. V(x) = -4x,² – 2x,² – x3² + 4x,x2 4. V(x) = -x,² – 4x,² – x3² + 4x2X3 %3D Please identify are these functions positive semi-definite, negative semi-definite, positive definite, negative definite or non-definite in the R' space?

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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Quadratic forms are given below. 1. V(x) = x,² + x2² + 3x3² – 2x1x2 2. V(x) = 5x,² + 2x2² + 3x3² + 2x1x2 3. V(x) = –4x,² – 2x2² – x3² + 4x,X2 4. V(x) = -x,² – 4x2² – x3² + 4x2X3 Please identify are these functions positive semi-definite, negative semi-definite, positive definite, negative definite or non-definite in the R’ space?
Transcribed Image Text:Quadratic forms are given below. 1. V(x) = x,² + x2² + 3x3² – 2x1x2 2. V(x) = 5x,² + 2x2² + 3x3² + 2x1x2 3. V(x) = –4x,² – 2x2² – x3² + 4x,X2 4. V(x) = -x,² – 4x2² – x3² + 4x2X3 Please identify are these functions positive semi-definite, negative semi-definite, positive definite, negative definite or non-definite in the R’ space?
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