1 -1 0 (b) Let B = -1 3 1 First show that B is positive definite and then 1 1 find the Cholesky decomposition of B.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Answer b

(a) Let A be a 6 x 6 real symmetric matrix which is negative definite. Let N
be the matrix obtained from A by deleting columns 2 and 5 and rows 2 and
5. Determine the sign of det N. Are the eigenvalues of N also eigenvalues of
A? Why?
1
-1 0
(b) Let B =
-1
3 1
First show that B is positive definite and then
%3D
1
1
find the Cholesky decomposition of B.
Transcribed Image Text:(a) Let A be a 6 x 6 real symmetric matrix which is negative definite. Let N be the matrix obtained from A by deleting columns 2 and 5 and rows 2 and 5. Determine the sign of det N. Are the eigenvalues of N also eigenvalues of A? Why? 1 -1 0 (b) Let B = -1 3 1 First show that B is positive definite and then %3D 1 1 find the Cholesky decomposition of B.
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