Which of the following are subspaces? Either show that they are, or explain why they fail to be.(a) The set of elements (x1,...,xn) with x2 1 −x2 = 0 inside Rn. (b) The set of elements (x1,...,xn) with 2x1 + 3x2 −4x3 = 0 inside Rn. (c) The set of elements (x1,...,xn) with x1 + x2 −x3 ≥ 0 inside Rn. (d) The set of elements (x1,...,xn) with x1 + x2 + 3 = 0 inside Rn. (e) The set of polynomials, with real coefficients, of the form a0 + a1x +···+ anxn such that a0 > a1 −2n, inside Pn. (f) The set of polynomials p, with real coefficients, such that p(1) + p(2) = p(5), inside Pn. (g) The set of matrices inside M(2,2) such that tr(M) = 0.2. For each of the following sets, either prove or disprove that it is a basis for the given vector space (you should state clearly any theorems or other standard results that you use). For those sets which are not bases, determine whether they are linearly independent, a spanning set, or neither. For R3: (a) {(2,4,5),(1,0,9),(1,8,−17)}. (b) {(1,5,7),(2,3,6),(4,0,9)}. (c) {(1,4,1),(−6,8,3)}. (d) {(1,1,1),(3,5,8),(2,7,6),(4,4,2)}.