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Consider the matrix M -4 7 8 7 3 11 8 -2 -2 5 11 -6 -9 -9-1 5 a For each vector from the following list -0-0-0-0 compute M. b What pattern do you notice in your answers to a? cIs M negative definite? How can you tell from your answers to a?

Consider the matrix M -4 7 8 7 3 11 8 -2 -2 5 11 -6 -9 -9-1 5 a For each vector from the following list -0-0-0-0 compute M. b What pattern do you notice in your answers to a? cIs M negative definite? How can you tell from your answers to a?

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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Consider the matrix M -4 7 8 -2 = 78 -2 3 11 5 11 -6 -9 -9-1 5 a For each vector from the following list 40-0-0-0 compute M. b What pattern do you notice in your answers to a? cIs M negative definite? How can you tell from your answers to a? d Use your computations to propose a condition that would help you check whether a matrix is negative definite. Is your condition necessary or sufficient or both?
Transcribed Image Text:Consider the matrix M -4 7 8 -2 = 78 -2 3 11 5 11 -6 -9 -9-1 5 a For each vector from the following list 40-0-0-0 compute M. b What pattern do you notice in your answers to a? cIs M negative definite? How can you tell from your answers to a? d Use your computations to propose a condition that would help you check whether a matrix is negative definite. Is your condition necessary or sufficient or both?
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