Exam1oldSol

The vectors 1 2 n are the columns of the matrix

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Unformatted text preview: he columns of the matrix A in part a) 1 2. (12 pts) Using Guassian elimination along with back substitution on the augmented matrix, solve the linear system 1 x 3 12 y 2 Ax  11 1 z 1 1  . 2 3 1 1 1 1 1 1 1 1 1 3  1 12 2 0 2 1 5 0 2 1 5 2 Ab 11 1 3 0 1 3 5 0 0 5/2 5/2 1  Ub z  1, 2y z  5 , y  2 x yz  1, x  2 x 2  y 2 z 1 a) Without doing any further calculations, write the LDU decomposition of the matrix A. The multipliers, in order, were 1 LDU  0 0  3, 21 10 31  2, 1 0 1 3 10 02 0 01 11 00 5 2 00 2 2 normalized to 1 by division, the pivots go into D ) 32  1/2 so 1 1 2 1 (the U here has had its pivots b) What sequence of elimination matrices E 1 , E 2 , . . , E k multiplying A on the left in turn, takes us from A to U in part a) (so that E k E k...
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This document was uploaded on 02/19/2014 for the course MATH 441 at WVU.

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