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

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

Answer 1

[Matt J]

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