Let Sij , Tij (c) and Ui(c) be the 3 3 matrices that you computed in Assignment 4.

(i) (2 points) Find the determinant of Sij for all i,j.

(ii) (3 points) Find the determinant of Tij(c) for any i,j. and c R. If you are having trouble doing this in general, you can compute the determinants of T12(1),T23(2), and T32(2) for half of the marks. These matrices will be used in part (iv).

(iii) (3 points) Find the determinant of Ui(c) for any i and c R. If you are having trouble doing this in general, you can compute the determinants of U1(2) and U3(1/3) for half of the marks. These matrices will be used in part (iv).

(iv) (2 points) Suppose that A is a 3 3 matrix and B is the matrix B = U1(2) T12(1) T23(2) U3(1/3) T32(2) S23 A.

If det(B) = 6, what is det(A)?