7. (a) Consider a hyperplane H = {(a1, a2, ..., an) ER": a, + a2 + ... + an = 0] Let e; = (0,0, ...,0,1,0, ...,0)T with 1 in the i-th position. Prove or disprove that " {el - e2, e2 - e3, ...) en-1 - ens is a basis of H". (b) The trace of a matrix is the sum along its diagonal elements. For A = (aij ), tr(A) = a11 + azz + ... + ann Using (a), or otherwise, find a basis of the subspace W = {A E Mnxn (R): tr(A) = 0}. Show all checking