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(a) For the following example, U = with a 0 and d‡0. Find x 0 such that a 0 0 b d 0 Ux=0 C 0 (b) Argue that for any dimension U, if one of the diagonal elements is zero, then there exists an x #0 such that Mx=0 Ux=0 (c) Conclude, based on the above arguments and PLU factorization, that if a matrix, M, is singular, then there exists an x 0 such that

(a) For the following example, U = with a 0 and d‡0. Find x 0 such that a 0 0 b d 0 Ux=0 C 0 (b) Argue that for any dimension U, if one of the diagonal elements is zero, then there exists an x #0 such that Mx=0 Ux=0 (c) Conclude, based on the above arguments and PLU factorization, that if a matrix, M, is singular, then there exists an x 0 such that

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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3. (a) For the following example, U = with a 0 and d ‡ 0. Find x ‡0 such that a b (33) 0 d e 0 00 Ux= = 0 (b) Argue that for any dimension U, if one of the diagonal elements is zero, then there exists an x ‡ 0 such that Ux=0 (c) Conclude, based on the above arguments and PLU factorization, that if a matrix, M, is singular, then there exists an x ‡ 0 such that Mx=0
Transcribed Image Text:3. (a) For the following example, U = with a 0 and d ‡ 0. Find x ‡0 such that a b (33) 0 d e 0 00 Ux= = 0 (b) Argue that for any dimension U, if one of the diagonal elements is zero, then there exists an x ‡ 0 such that Ux=0 (c) Conclude, based on the above arguments and PLU factorization, that if a matrix, M, is singular, then there exists an x ‡ 0 such that Mx=0
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