1. Let 1 -1 3 -1 2 -1 3 -1 13 (a) Are the matrices A, B positive definite, non-negative definite, or neither? (b) For what range of values of 3 is the matrix C positive definite? A 2 -2 1 1 »-(1) -(HH). B = 0 C = 1 2 1 -2 2 1 1 =
1. Let 1 -1 3 -1 2 -1 3 -1 13 (a) Are the matrices A, B positive definite, non-negative definite, or neither? (b) For what range of values of 3 is the matrix C positive definite? A 2 -2 1 1 »-(1) -(HH). B = 0 C = 1 2 1 -2 2 1 1 =
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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Transcribed Image Text:1. Let
1 -1 1 3
2
1 1 1
~() --(17) <-(H)
).
A = -1 2 −1
0
1 2 1
3 -1 13
-2 0 2
1 1
B =
(a) Are the matrices A, B positive definite, non-negative definite, or neither?
(b) For what range of values of ß is the matrix C positive definite?
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