small question about gram schmidt

Question

I tried to find an answer online first, so excuse me if this question was asked before,

but, is the result of the gram schmidt process different, depending on the order that I go over the vectors in the original group?

I think it is, but i could not find a formal proof for it...

Thanks!

Answer 1

Indeed it is. Try running the proces on $[1,0]$ and $[1,1]$ in two different orders.