Let S1 span100 110 and S2 span001010 be a subspaces of R3

Let S_1 = span((1,0,0), (1,1,0)) and S^2 = span((0,0,1),(0,1,0)) be a subspaces of R^3. Determine the dimension and a basis for the subspace S_1 S_2.

A vector in S1 is:

a(1,0,0)+b(1,1,0)=(a+b,b,0)

A vector in S2 is:

r(0,0,1)+s(0,1,0)=(0,s,r)

So a vector in intersectin would be:

(a+b,b,0)=(0,s,r)

Hence, r=0

a+b=0

So the vector is:

s(0,1,0)

Hence it is spanned by just one vector so dimension is 1

Basis is {(0,1,0)}