Consider the complex-valued matrix V = [ v(1) v(2) v(3) v(4) ] = 2 3 + jc 8 a + jb a + jb 2 3 + jc 8 8 a + jb 2 3 + jc 3 + jc 8 a + jb 2 (i) (6 pts.) Show that there exists only one choice of constants a R, b R and c > 0 such that the columns of V are pairwise orthogonal. For that choice of a, b and c, what are the resulting column norms? (You will need to set two column inner products equal to zero. Check your answers in MATLAB using V'*V before proceeding further.) From now on, assume that a, b, c and d are as found in part (i) above. (ii) (6 pts.) Determine d such that the real-valued vector s = [ 27 45 41 23 ]T equals Vd. (Gaussian elimination is not needed here. Again, verify your answers in MATLAB.) (iii) (5 pts.) Determine the projection s of s onto the subspace generated by the vectors v(2) and v(4). What is the value of s s2? (iv) (3 pts.) If x = v(1) + 2jv(2) + v(3) +