Prove that in any vector space k × 0 = 0, where k is any real number and 0 is the zero vector.
I know I have to use the vector axioms..
AxiomSignificationAssociativity of additionu + (v + w) = (u + v) + w.Commutativity of additionv + w = w + v.Identity element of additionThere exists an element 0 ∈ V, called the zero vector, such that v + 0 = v for all v ∈ V.Inverse elements of additionFor 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 multiplicationa(bv) = (ab)v [nb 3]Identity element of scalar multiplication1v = v, where 1 denotes the multiplicative identity in F.
Do I use the distributivity of scalar multiplication with respect to field addition ??
little confused since it's pretty much obvious!