1. The problem statement, all variables and given/known data Does this set describe a vector space? Te set of all solutions (x,y) of the equation 2x + 3y = 0 with addition and multiplication by scalars defined as in R^2. 2. Relevant equations Associativity of addition u + (v + w) = (u + v) + w. Commutativity of addition v + w = w + v. Identity element of addition There exists an element 0 ∈ V, called the zero vector, such that v + 0 = v for all v ∈ V. Inverse elements of addition For all v ∈ V, there exists an element w ∈ V, called the additive inverse of v, such that v + w = 0. The additive inverse is denoted −v. Distributivity of scalar multiplication with respect to vector addition a(v + w) = av + aw. Distributivity of scalar multiplication with respect to field addition (a + b)v = av + bv. Compatibility of scalar multiplication with field multiplication a(bv) = (ab)v [nb 3] Identity element of scalar multiplication 1v = v, where 1 denotes the multiplicative identity in F. 3. The attempt at a solution Could not find one counterexample. Since I obviously can not go through every solution to prove this is a valid vector space, there must be a counterexample or some equation (that I'm not aware of) that proves that every solution of this equation is a valid vector space.