Error "Matrix dimensions must agree" in the line "T = norm(rref(Y)- rref(U)) < tol;" I used "A=[1 1 4;0 -4 0;-5 -1 -8; 2 3 -1] [L,U] = eluinv(A);" in my livescript. Thank you so much!

Here is the function.m:

function [L,U] = eluinv(A)
[m,n] = size(A);
[L,U] = lu(A);
B = L*U;
 
C = closetozeroroundoff(B,7);
q = closetozeroroundoff(A,7);
if q == C
  disp('Yes, I have got LU factorization');
end
 
Y = closetozeroroundoff(A,7);
tol = 1e-6;
T = norm(rref(Y)- rref(U)) < tol;
 
if T
 disp('U is an echelon form of A');
else
 disp('Something is wrong')
end
 
if rank(A) ~= n
 sprintf('A is not invertible');
 invA = [];
 return
else
 invL = eye(n)/rref(L);
 invU = eye(n)/rref(U);
 invA = invU * invL;
end
P = inv(A);
J = closetozeroroundoff(P,7);
Q = closetozeroroundoff(invA,7);
if J == Q
 disp('Yes, LU factorization works for calculating the inverses');
else
 disp('LU factorization doesnt work for me');
end
 
  
 

[KSSV]

What is closetozeroroundoff?

[KSSV]

IN the line:

T = norm(rref(Y)- rref(U)) < tol;

Check the dimensions of Y and U..it looks they are different; thus the error.

[Tianlan Yang]

Hi , here is the closetozeroroundoff function:

function B=closetozeroroundoff(H,p)

H(abs(H)<10^-p)=0;

B=H;

end

[Tianlan Yang]

Could you please show how to make it work? Because I try 3*4 matrix, it works, but when I try 4*3 matrix, it shows error. Thank you!

Answer 1

[KSSV]

Replace the line:

T = norm(rref(Y)- rref(U)) < tol;

with

T = (norm(rref(Y))- norm(rref(U))) < tol;

[Tianlan Yang]

That works. Thank you.