(1) Let A = [ X 0 ] where X and Z are square
            [ Y Z ]
    Show that det(A) = det(X)*det(Z)

(2) Let A be an n by n lower triangular or upper triangular matrix.
    Show that det(A) = product_{i=1 to n} A_ii
  
(3) Sec 4.2: 1 (with justifications), 26, 30
 
(4) Sec 4.3: 1 (with justifications), 10, 11, 12, 13, 15, 17, 22(c), 24