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Unformatted text preview: original Gaussian Algorithm can have multipliers no larger than one in absolute
value. 2. Find the general solutions of the systems whose augmented matrix is: 0 2 4 0 6 1 3 4 1 12 1 3 4 1 12 1 3 4 1 12 0 2 4 0 6 0 2 4 0
6 2 4 0 0 6 2 4 0 0 6 0 10 8 2 30 1 3 4 1 12 1 3 4 1 12 1 0 2 1 3 0 1 2 0
3 0 1 2 0
3 0 1 2 0 3 0 10 8 2 30 0 0 12 2 0 0 0 12 2 0 1
3 1 0 0 2 / 3 3
1 0 2
0 1 2 0
3 0 1 0 1/ 3 3 0 0 1 1/ 6 0 0 0 1 1/ 6 0 Thus x4 is free, x3 0 (1/ 6) x4 x4 / 6, x2 3 (1/ 3) x4 3 x4 / 3, and x1 3 2 / 3x4 3 2 x4 / 3.
3. Show that if there are two distinct solutions to a linear system of equations then there is an
infinite set of solutions. More specifically, show that if Ax b and Ay b , then for any scalar , A( x (...
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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.
 Spring '08
 PAVLOVIC
 Matrices

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