Need help with subspace basis

I'm writing a script to find the basis of subspace spanned by a vector set and by a homogenous system. In the case with the vector set, I plan to put my given matrix through rref to find the pivots and from there point out the vectors that are the bases.

Here's what I got so far

disp('input matrix')

A = input('A=')

Ar = rref(A)

s = size(Ar)

s1=s(1)

s2=s(2)

for i=1:s1

for i=1:s2

if Ar(i)== 1

A(:,i)

end

end

end

[KALYAN ACHARJYA]

for i=1:s1
    for i=1:s2
        
    end

Is both are "i"?

[Jacked Daniel]

yeah but they I don't think it matters, I changed it to t and had the same results. I also used two i(s) before for two different for loops and it was fine then.

Answer 1

[Matt J]

You could just use orth()

[Jacked Daniel]

I read the description of the orth command, at first it seemed like the "Easy button" for me but the values it returns are not what I expected. I still can't fully understand how the orth command works and the basis it returns is completely different from what I get solving by hand.

[Matt J]

You do realize that the basis for any linear space is non-unique, right?

[Jacked Daniel]

Yes and are you suggesting that the ugly combination of entries I received is a basis? I do agree but I can't show that to my teacher cause she's gonna check and compare my MATLAB basis to her do-it-by-hand basis. So I can't use the orth command BUT the null command I use for the case of subspace spanned by homogenous systems is quite handy. It returns the exact value I expect it would. Oh and I figured out how to work the code, I added a "break" command and it is looking good. Thanks for helping me.