MatLab: Write a function that will accept a matrix and return a matrix. The func

Question

MatLab: Write a function that will accept a matrix and return a matrix. The function should take the passed matrix and using Gauss Elimination put zeros in the first column of the matrix. The first step is to put the row with the largest absolute value in the first row by swapping rows using functions you have already created. Then calculate the factor necessary to multiply the first row by so that when it is added to the second row, the element in row 2 column 1 becomes zero. Use your linear combination function to accomplish this task. Then move down to the next row. Keep looping through the rows until all the elements in column 1, except row 1, are zero. The function should work with any size matrix—not necessarily square.

For example, if the matrix

is passed to the function, the function would return

Explanation / Answer

matlab code

function [x,U]=gausselim(A,b)

% function to perform gauss eliminination

%FORWARD ELIMINATION

n=length(b);

m=zeros(n,1);

x=zeros(n,1);

for k =1:n-1;

%compute the kth column of M

m(k+1:n) = A(k+1:n,k)/A(k,k);

%compute

%An=Mn*An-1;

%bn=Mn*bn-1;

for i=k+1:n

A(i, k+1:n) = A(i,k+1:n)-m(i)*A(k,k+1:n);

end;

b(k+1:n)=b(k+1:n)-b(k)*m(k+1:n);

end

U= triu(A);

%BACKWARD ELIMINATION

x(n)=b(n)/A(n,n);

for k =n-1:-1:1;

b(1:k)=b(1:k)-x(k+1)* U(1:k,k+1);

x(k)=b(k)/U(k,k);

end

end

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