Indicate whether each of the following statements istrueorfalse.Provide a shortjustification(i.e. definition, short proof, counterexample, etc.) for each.

(a). Any system of n equations in n unknowns has at most n solutions. (b). A homogeneous system of linear equations is always consistent. (c). If {u, v, w} is linearly dependent, then u E span { v, w }. (d). S = ((x, y) ER' : x2 + y2 = 0} is a subspace of R2. (e). If V is a vector space with dim(V) = n, and S = {V1, V2, ... . V,} is a linearly independent subset of V, then S is a basis for V. (f). Any set of n vectors in R" is a spanning set for R" (g). If M is an m x n matrix with m > n, then the rank of A is at most m