Assume that we want to determine whether the set of all 2×3 matrices of the form [a a−12b b b 8a −9a 0] where a and b are real numbers, together with the standard operations form a subspace of is a subspace of V=M2×3, the set of all 2×3 matrices. To this aim, we will check if 0∈W , then check whether each of the 2 axioms given in the Test for a Subspace theorem is satisfied using the inherited operations from W (standard operations). Let u and v be two elements (matrices) in W and c be any real number. Does W together with the standard operations form a vector subspace of R4?