What do you mean by x^2, x^3 ?

If You acquire the notation:

(x^1, x^2, x^3)

for a generic element of Your space than the condition

x^2 + x^3 = 0

means that the generic element of given subspace is of the form

x^1(1,0,0)+x^2(0,1,-1)

Observe that A*(1,0,0) = (1,1,1) which is not an element of our subspace...

So, explain the notation or give us some clue