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**Unformatted text preview: **Math 400 Assignment #1 -- Systems of Linear Equations 17 17 3 3 3 3 3 3 Find an approximate numerical solution to the system with 10 10 10 10 10 1 10 10 10 1 and = 1 1 10 10 2 1 1 1 10 3------ = Ax = b A b a) using basic Gaussian elimination b) using Gaussian elimination with partial pivoting c) using Gaussian elimination with (partially) scaled partial pivoting in each case compute the residual error vector . Compare your results for the three methods. For part a) try to find the precise step at which a large error is introduced. r = b - Ax 1. 2. In Gauss-Jordan Elimination the i th equation is used to eliminate the i th unknown from all of the equations except the i th. This is similar to Gaussian elimination, but in this method the augmented matrix for the linear system is reduced from A = x b [ ] (1) (1) (1) (1) 11 12 1 1 1 (1) (1) (1) (1) 21 22 2 2 1 (1) (1) (1) (1) 1 2 1 | n n n n n n n n nn a a a a a a a a A a a a a + + + = b (1) (1) 11 1 1 (2) (2) 22 2 1 ( ) ( ) 1 n n n n nn n n a a a a a a + + + to The solution is obtained by setting...

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