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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.

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
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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(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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