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Use one of the equiv statements to conclude that the matrix below is not a positive definite matrix. Explain! B = 1 2 3 204 341

Use one of the equiv statements to conclude that the matrix below is not a positive definite matrix. Explain! B = 1 2 3 204 341

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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Definition A matrix A E R"x" is said to be positive definite if it is symmetric and has an LU factorization in which each pivot is positive. The following statements are equivalent: (i) A is positive definite. A can be factored as A diagonal entries. TAx> 0 for all nonzero xER". Use one of the equiv statements to conclude that the matrix below is not a positive definite matrix. Explain! - RTR where R is an upper triangular matrix with positive B = 1 2 3 204 3 4 1
Transcribed Image Text:Definition A matrix A E R"x" is said to be positive definite if it is symmetric and has an LU factorization in which each pivot is positive. The following statements are equivalent: (i) A is positive definite. A can be factored as A diagonal entries. TAx> 0 for all nonzero xER". Use one of the equiv statements to conclude that the matrix below is not a positive definite matrix. Explain! - RTR where R is an upper triangular matrix with positive B = 1 2 3 204 3 4 1
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Given : B=123204341

To Explain : B is Not positive definite 

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