Question

Decide if the given subset W of the vector space V is or is not a subspace of V. If not, identify at least one requirement that is not satisfied.
V=R^3 W=(x1,x2,x3) x3=0

Answer 1

W is a subset of V
since (a,b,0)-(c,d,0)=(a-c,b-d,0)
The difference of two elements of W is and element of W.