To do this problem, you should first go through the code for the GaussianElimina

Question

To do this problem, you should first go through the code for the GaussianElimination function, and understand it. Then write a function that solves the system of equations for the case where the equation matrix is upper-triangular. The function header is given as: function x = SolveUpper (U,b) where the input U is an upper-triangular matrix, and 6 is a column vector; the output x is the solution to Ux = b. (Hint: if the system begins with a matrix U which is already in an upper-triangular form, we do not need to do elimination at all; hence only the back-substitute part from the GaussianElimination function is needed.)

Explanation / Answer

MATLAB command that directly computes backward substitution.

Programs:
CODE 1:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function x=backsub(A,y);
% backsub: solves upper triangular system A*x = y using backwards
substitution
% usage: x=backsub(A,y);
%
% arguments:
% A (nxn) - upper triangular matrix
% y (nx1) - vector
%
% x (nx1) - solution to A*x = y

CODE 2: If you don't want to use direct command

% check to see that A is upper triangular
if any(any(tril(A,-1)))
   error('A must be upper triangular')
end

% check dimensions of A and y
[n,m]=size(A);
if n~=m
   error('A must be square');
end
if any([n 1]~=size(y))
   error('y must be a vector with the same # of rows as A');
end

% perform backwards substitution
x=zeros(n,1);
x(n)=y(n)/A(n,n);
for i=n-1:-1:1
   x(i)=(y(i)-A(i,i+1:n)*x(i+1:n))/A(i,i);
end

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