Question

determine whether or not the following subsets are subspaces of R3, explain:

X=[x1,x2,x3] : x1+x2+x3=0
X=[x1,x2,x3] : x1+x2+x3=1
X=[x1,x2,x3] : x1x2x3=0
X=[x1,x2,x3] :-x1+2x2+x3=0 and x1+3x2+3x3=0