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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Let
3
1 -1
-1 2 -1
3 -1 13
(a) Are the matrices A, B positive definite, non-negative definite, or neither?
2 1 -2
1
1
1
»-(HD) -(H)
B = 1 1 0
C= 1
2
1
-2
2
1
1
A =
(b) For what range of values of ß is the matrix C positive definite?
Transcribed Image Text:1. Let 3 1 -1 -1 2 -1 3 -1 13 (a) Are the matrices A, B positive definite, non-negative definite, or neither? 2 1 -2 1 1 1 »-(HD) -(H) B = 1 1 0 C= 1 2 1 -2 2 1 1 A = (b) For what range of values of ß is the matrix C positive definite?
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