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Unformatted text preview: y x)) b.
If Ax b and Ay b then A( y x) Ay Ax b b 0 and for any scalar ,
A( x ( y x)) Ax A ( y x) Ax A( y x) b 0 b.
4. Suppose you are to solve m different linear systems of n equations in n unknowns. All of the
equations have the same matrix, however, they just differ in right hand sides. Estimate how many
multiplications are required. n3
multiplications and each of the m different
3
n3
2 mn 2 multiplications.
linear systems requires n multiplications for a total of
3
The elimination step on the matrix requires 5. Use the Gaussian Elimination with Partial Pivoting and Solution algorithm to solve
3x1 5 x2 2 x3 16 3x1 x3 5 6 x1 2 x2 4 x3 8
Show what occupies storage in the A matrix and the ip array initially and after each major step of
elimination. A ip 3
3
6 5
0
2 2
1
4 ?
?
? 6 2 4 1/2 1 1 1/2 4 4 3
?
? 6
1/2 2
4 1/2 1/4 4
4
2 3
3
? 6 2 4 3 1/2 4 3 1/2 1/4 4...
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This test prep was uploaded on 03/21/2014 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas at Austin.
 Spring '08
 PAVLOVIC
 Matrices

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