6. Let S = {11.1, 152,153} be an ordered basis for a subspace V E R4 with illxDCDrt (i) [3 marks] Apply GramSchmidt process to convert S into an orthonor mal basis for V. Show all your workings clearly (follow the algorithm in theorem 5.2.19 exactly). 1 5 1 2 (ii) [3 marks] Let U) = . Find the projection of w onto the subspace V. (iii) [2 marks] Find a unit vector n such that for all u E V, n - u = 0. (iv) [4 marks] Is it possible to nd a nonzero vector n' such that (a) for all u E V, n' - u = 0, and (b) {'n, n'} is linearly independent, Where n is the unit vector in (iii)