Homework 8 Solution

Homework 8 Solution - Lecture 8 MEEN 357 Homework Solution...

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Lecture 8 MEEN 357 Homework Solution 1 Lecture-08-Homework-Solution-2009.doc RMB 1. Modify the script on page 11 above so that it will implement the Gauss-Jordan method for the same problem, i.e., for the same A and b . Solution : The script on page 11 is %Primitive Gaussian Elimination for n=3. clc clear all %Enter the Matrix A a 3X3 A=[1,3,1;2,1,1;-2,2,-1] %Enter the Matrix b a 3X1 b=[1;5;-8] %Form the Augmented Matrix <A|b> M=[A,b] %Step 1: Build zeros below M(1,1) %The next line checks if M(1,1) is zero. If so, the %calculation stops. if M(1,1)==0,error( 'You tried to divide by zero' ), end for n=[2 3] M(n,:)=M(n,:)-(M(n,1)/M(1,1))*M(1,:); end %Step 2: Build zeros below the new M(2,2) if M(2,2)==0,error( 'You tried to divide by zero' ), end for n=3 M(n,:)=M(n,:)-(M(n,2)/M(2,2))*M(2,:); end if M(3,3)==0,error( 'You tried to divide by zero' ), end x3=M(3,4)/M(3,3) x2=(M(2,4)-M(2,3)*x3)/M(2,2) x1=(M(1,4)-M(1,3)*x3-M(1,2)*x2)/M(1,1) The last three lines represent the back substitution phase of Gaussian Elimination. When one adopts Gauss-Jordan elimination, this step is replaced by row operations that built zeros above the (3,3) element and, next, above the (2,2) element.
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This note was uploaded on 07/28/2010 for the course MEEN 357 taught by Professor Anamalai during the Fall '07 term at Texas A&M.

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Homework 8 Solution - Lecture 8 MEEN 357 Homework Solution...

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