write a Matlab function file to solve system Ax=b byusing the output of the function lufac2a your function should haveinputs f=matrix return from lufac2a, piv=array return by lufac2aand b=right hand side of your system.the only output for yoursystem should be x

guideline

1.use the column access for the matrixentries

2. do not create any other matrix in your function-getyour data directly from the matrix passed into yourfunction

3.do not use Matlab command designed for solvingsystem

function file LUFAC2A GIVEN BELOW

function [f, rp, flag] = lufac2a(a)

% The purpose of this function is to apply Gaussianelimination with

% partial pivoting to the input matrix a . (Thisfollows the LINPACK

% algorithm except uses elementary Gaussiantransformations from Matrix

% Computations). This function returns:

%

% f - matrix containing the information about the Land U matrices in the

% factorization PA=LU

%

% rp - array containing information about the rowinterchanges used in the

% elimination process

%

% flag - error flag (set to 0 if a is invertible, andset to k>0 if a

% nonzero pivot could not be found for columnk)

%

% The calling sequence is [f, rp, flag] =lufac2(a)

[m,n] = size(a);

if m ~= n

disp('The matrix must be a square matrix.')

return

end

f = a;

rp = zeros(n,1);

for j=1:n-1

[mx,p] = max(abs(f(j:n,j)));

if mx == 0

flag = j;

return

end

p = p + j - 1;

rp(j) = p;

if p~=j

temp = f(j,j:n);

f(j,j:n) = f(p,j:n);

f(p,j:n) = temp;

end

i=(j+1):n;

f(i,j) = f(i,j)/f(j,j);

f(i,i) = f(i,i) - f(i,j)*f(j,i);

end

if f(n,n)==0

flag = n;

else

flag = 0;

end

return