Which vectors we can use to form a basis of the given space

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Hi everyone,
I am learning linear algebra in MATLAB. I am having my matrix A:
A = [1,0,2,3; 4,-1,0,2; 0,-1,-8,-10];
I am supposed to find the vectors that form a basis of the given space. As it is clear, the given space will be 3. So, when I converted it to reduce echelon form using rref(A) I got the following matrix:
rref(A)
ans =
1 0 2 3
0 1 8 10
0 0 0 0
Now, I am confused that which vector should I choose to form a basis of the given space? Should it be Basis for col(A) or Basis for row(A)? I am so confused at it. I will highly appreciate any help. Thanks in advance

Accepted Answer

Matt J
Matt J on 30 Aug 2022
One solution is to use orth:
A = [1,0,2,3; 4,-1,0,2; 0,-1,-8,-10];
basis=orth(A)
basis = 3×2
-0.2710 -0.1940 -0.1305 -0.9630 0.9537 -0.1869

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