Show that two sets of vectors span the same subspace

1. Dec 14, 2011

csc2iffy

1. The problem statement, all variables and given/known data
Show that the two sets of vectors
{A=(1,1,0), B=(0,0,1)}
and
{C=(1,1,1), D=(-1,-1,1)}
span the same subspace of R3.

2. Relevant equations
{A=(1,1,0), B=(0,0,1)}
{C=(1,1,1), D=(-1,-1,1)}

3. The attempt at a solution
aA+bB=(a,a,0)+(0,0,b)=(a,a,b)
aC+bD=(a,a,a)+(-b,-b,b)=(a-b,a-b,a+b)
I am confused because I thought the answers would turn out to be equal.. Is this not the way to do it?

2. Dec 14, 2011

Well, take (a-b, a-b, a+b). Now, this equals a(1, 1, 1) + b(-1, -1, 1). Of what form are the vectors (1, 1, 1) and (-1, -1, 1)? Do they look familiar?

3. Dec 14, 2011

csc2iffy

its aC+bD... i don't understand how this is related to aA+bB??

4. Dec 14, 2011