5. Bras and kets. 5 points] Consider a three-dimensional Hilbert space with an orthonormal basis (1), (2), 13). Using complex constants a and b define the kets [20) = a|1) -b/2) + a|3) ; (0) = b/1) + a|2) . (a) Write down (] and ($). Calculate (oly) and (vo). Check that (oly) = (w/6)*. (b) Express () and (o) as column vectors in the (1), (2), (3) basis and repeat (a). (c) Let A = (o) (#). Find the 3 x 3 matrix that represents A in the given basis. (d) Let Q = (v)(#| + |0) (o). Is Q hermitian? Give a simple argument (no compu- tation) to show that Q has a zero eigenvalue