Question

Define a vector subspace of a vector space V

Answer 1

If V is a vector space over a field K and if W is a subset of V, then W is a vector subspace of V if under the operations of V, W is a vector space over K. Equivalently, a nonempty subset W is a vector subspace of V if, whenever w₁, w₂ are elements of W and α, β are elements of K, it follows that αw₁ + βw₂ is in W.