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Determine whether each of the following matrices is positive definite. If it is not, give a submatrix and determinant that demonstrates this. A₁ is not positive definite: 0 -1 1 1 A₁ = -1 1 1-2 1 -2 2 1 -1 1 A₂ 1 4 0 1 01 = A3 = 10 -1 032 -1 2 10 3 0 -1 -1 1 det -1 1 -2 = 0 1 -2 2 < Select an answer > < Select an answer > A2 is positive definite A2 is not positive definite: < Select an answer >

Determine whether each of the following matrices is positive definite. If it is not, give a submatrix and determinant that demonstrates this. A₁ is not positive definite: 0 -1 1 1 A₁ = -1 1 1-2 1 -2 2 1 -1 1 A₂ 1 4 0 1 01 = A3 = 10 -1 032 -1 2 10 3 0 -1 -1 1 det -1 1 -2 = 0 1 -2 2 < Select an answer > < Select an answer > A2 is positive definite A2 is not positive definite: < Select an answer >

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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Determine whether each of the following matrices is positive definite. If it is not, give a submatrix and determinant that demonstrates this. A₁ is not positive definite: 0 -1 1 1 A₁ = -1 1 1-2 1 -2 2 1 -1 1 A₂ 1 4 0 1 01 = A3 = 10 -1 032 -1 2 10 3 0 -1 -1 1 det -1 1 -2 = 0 1 -2 2 < Select an answer > < Select an answer > A2 is positive definite A2 is not positive definite: < Select an answer >
Transcribed Image Text:Determine whether each of the following matrices is positive definite. If it is not, give a submatrix and determinant that demonstrates this. A₁ is not positive definite: 0 -1 1 1 A₁ = -1 1 1-2 1 -2 2 1 -1 1 A₂ 1 4 0 1 01 = A3 = 10 -1 032 -1 2 10 3 0 -1 -1 1 det -1 1 -2 = 0 1 -2 2 < Select an answer > < Select an answer > A2 is positive definite A2 is not positive definite: < Select an answer >
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