SOLUTIONS+TO+HW3+revised

SOLUTIONS+TO+HW3+revised - SOLUTIONS TO HW3 Part 1 1 n1...

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SOLUTIONS TO HW3 Part 1 1. n1 + nc2H4 = 75 n2 + n0 = 25 * for mixing point 2n1+ 2n3+2n4 = 150 2n2+n3+2n4+n5=50 4n1+4n3+2n5=300 n 1 = 75(0.8) = 60 n 3 – 4.5n4 = 0 2.A = [1 0 0 0 0 1 0;0 1 0 0 0 0 1;2 0 2 2 0 0 0;0 2 1 2 1 0 0 ;4 0 4 0 2 0 0 ;1 0 0 0 0 0 0;0 0 1 -4.5 0 0 0] b=[75;25;150;50;300;60;0]; x =[n1,n2,n3,n4,n5,n6,n7] 3) Matlab code for Gaussian Elimination function x = mygehw3_nita3(a,b) n = length(b); x = zeros(size(b)); % Forward elimination step of Gauss elimination for k = 1:n-1 if (abs(a(k,k)) < 1e-12) [val, index] = max(abs(a(k+1:n,k))); tmpA = a(k,:); tmpB = b(k); a(k,:) = a(index+k,:); b(k) = b(index+k); a(index+k,:) = tmpA; b(index+k) = tmpB; end % Eliminate our variable in each row for i = k+1:n % Find pivot fctr = a(i,k)/a(k,k); % For each column in the row being eliminated, subtract the initial % value times the pivot for j = k+1:n a(i,j) = a(i,j) - fctr*a(k,j); end % Don't forget to do that for the b vector as well b(i) = b(i) - fctr*b(k); end end % Backward substitution step if (abs(a(n,n)) < 1e-12) error('Divide by zero error in back substitution.') end % Do back substitution to get x_n x(n) = b(n)/a(n,n); for i = n-1:-1:1 sum = b(i);
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