1. Let V be a finite dimensional vector space over a field F. 1) Define what it means for a collection of vectors v₁, . . . , v_m in V to be linearly independent. 2) Give an example of a vector space over R that is not a subspace of Rⁿ. No justification is required. 3) Let = {v₁, . . . , v_n} be a basis for V . For a vector v V , define the coordinates [v] of v. (The textbook writes M(v, ) instead of [v]). 4) Suppose that U₁, . . . , U_n are subspaces of V . Explain the meaning of the statement V = U₁ U_n.