A.)

function x = Tridiag(e,f,g,r) % Tridiag: Tridiagonal equation solver banded system % x = Tridiag(e,f,g,r): Tridiagonal system solver. % input: % e = subdiagonal vector % f = diagonal vector % g = superdiagonal vector % r = right hand side vector % output: % x = solution vector n=length(f); % forward elimination for k = 2:n factor = e(k)/f(k-1); f(k) = f(k) - factor*g(k-1); r(k) = r(k) - factor*r(k-1); end % back substitution x(n) = r(n)/f(n); for k = n-1:-1:1 x(k) = (r(k)-g(k)*x(k+1))/f(k); end

B.)

function x = GaussPivot(A,b) % GaussPivot: Gauss elimination pivoting % x = GaussPivot(A,b): Gauss elimination with pivoting. % input: % A = coefficient matrix % b = right hand side vector % output: % x = solution vector [m,n]=size(A); if m~=n, error('Matrix A must be square'); end nb=n+1; Aug=[A b]; % forward elimination for k = 1:n-1 % partial pivoting [big,i]=max(abs(Aug(k:n,k))); ipr=i+k-1; if ipr~=k Aug([k,ipr],:)=Aug([ipr,k],:); end for i = k+1:n factor=Aug(i,k)/Aug(k,k); Aug(i,k:nb)=Aug(i,k:nb)-factor*Aug(k,k:nb); end end % back substitution x=zeros(n,1); x(n)=Aug(n,nb)/Aug(n,n); for i = n-1:-1:1 x(i)=(Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i); end

(1) (2 points) Consider the following system of equations: 0.8x1-0.4x2-41 0.4x1+0.8x2-0.4x3 = 25 -0.4x2 + 0.8x3 = 105 (a) Use MATLAB TriDiag function to solve this system (See Section 9.5 for an example on how to use this function) (b) Use MATLAB GaussPivot function and MATLAB "" operator to verity your results from part (a)