Assess students' recall of the vector space axioms for real vector spaces: require them to state the axioms formally (closure under addition and scalar multiplication; commutativity and associativity of addition; additive identity and inverses; distributivity of scalar sums and vector sums; compatibility of scalar multiplication with field multiplication; existence of multiplicative identity), and to classify brief examples and non-examples (e.g., R^n, polynomials, a subset failing closure) with one-sentence justifications.