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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.
 Spring '08
 STAFF
 Math, Linear Algebra, Algebra

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