Question

For “Extract the column basis”, using the MATLAB functions rref and rank, make your own function file to find pivot columns of A from the result of rref(A).
Do NOT use the syntax [R pivotcols] = rref(A), use only rref(A). You may use the MATLAB commands min and find.please follow the instructions!! please help me , I have to submit in 2 hours

Answer 1

Solution

answer = questdlg('What do you want?', ...

'Matrix analysis', ...

'Fundamental space','Extract the column basis','QR decomposition');

% Handle response

switch answer

case ' Fundamental space '

A=[2,-1,3,5;4,-3,1,3;3,-2,3,4;4,-1,15,17;7,-6,-7,0];

[V, pivot] = rref(A)

r = length(pivot)

cs = A(:,pivot)

ns = null(A,'r')

rs = V(1:r,:)'

lns = null(A','r')

disp([answer])

case ' Extract the column basis '

A=[2,-1,3,5;4,-3,1,3;3,-2,3,4;4,-1,15,17;7,-6,-7,0];

fnc1()

disp([answer])

    case ' QR decomposition '

A=[2,-1,3,5;4,-3,1,3;3,-2,3,4;4,-1,15,17;7,-6,-7,1];

func2.m

disp([answer])

end

fnc1.m : function file for Extract the column basis

fnc1.m

function [Asub,idx]=licols(A,tol)

%Extract a linearly independent set of columns of a given matrix A

     if ~nnz(A) %A has no non-zeros and hence no independent columns

         Asub=[]; idx=[];

         return

     end

     if nargin<2, tol=1e-10; end

       [Q, R, E] = qr(X,0);

       if ~isvector(R)

        diagr = abs(diag(R));

       else

        diagr = R(1);  

       end

       %Estimation of Rank

       r = find(diagr >= tol*diagr(1), 1, 'last');

       idx=sort(E(1:r));

       Asub=A(:,idx);

func2.m

l=func2(A)

[m, n] = size(A); Q = zeros(m, n); R = zeros(n, n);

for j=1:n
v=A (:,, j);
for i1:j-1
R(i,j)=Q(: ,i)‘*A(: j);

v=v—R(i,j)*Q(:,i);
R(j,j)=norm(v);
Q(: ,j)=v/R(j,j);
end

Feel free to reach out regarding any queries . And please do rate the answer . Thank you .