I am given 4 vectors that span a subspace S of R^4.
w1 = (1,0,2,1)^T
w2= (1,1,2,0)^T
w3= (2,1,4,1)^T
w4 = (3,2,6,1)^T
I need to find the basis and dimension of S.
Here is what I get for my reduced row echelon form:
1 0 1 1
0 1 1 2
0 0 0 0
0 0 0 0
then i set the lead variables equal to the free variables and I get
x1 = -x3 - x4
x2 = -x3 - 2x4
so i think the basis would be {(-1,-1,1,0)^T,(-1,-2,0,1)^T}
but the answer says it is {(1, 0, 2, 1)^T, (0,1,1,2)^T)}
i know there can be more than one basis, is she just using that basis because it is w1 and w2? is my basis also a correct answer? thanks a lot.