(a) Let A, B be 5x5 matrices such that det (A) = R+3 and det (B) =-3. Find the following. (i) det 2(A 'B)') (ii) det (adj (B')) (b) Find all the value(s) of x for which each of the following matrices is non-singular. X- 1 -X X (i) C= -1 2x -x -2x 2-x 1 3 21 1 -5 Ox0 (ii) M = 7 x0 3 3 2 1 4 0 1 1 1 1 0 1-h (c) Let N= 0 1 h h where h is a constant. h (i) By reducing N to an upper triangular form with elementary row operations, find det (N) in terms of h. (ii) Use the result of (c)(i) to determine if the following system of linear equations is consistent. Justify your answer. XA 1, 2X3 = 0. 3X, + 3X 6, 3x + + XA 9