Question

determine if v1= [ 2 1 0] v2=[ -1 1 3] v3=[ 0 -1 6] spans the vector space of rows with three real entries which has dimension 3.

so I wanted to make sure I did this correct. First I created a matrix with v1,v2,v3 as the columns (so for example column 1= 2
1
0

then I created an augmented matrix with that by tacking on the column [0;0;0]

I reduced it to the rref and found that it created the identity matrix so a1=0 a2=0 and a3=0. So does this mean it spans V , where V has the dimension 3?