Answer to Quiz 5 Fri 23 Sep 2005

     [  2  -3   4  ]
 A = [  4  -7  13  ].
     [ -2   0   9  ]

1. Compute the LU factorization of A. Write the matrices L and U.

   Answer:

                   4       [                ]
       R2 := R2 - --- R1   [  2   -3    4   ]
                   2       [                ]
    A -------------------> [  2   -1    5   ]
                   -2      [                ]
       R3 := R3 - --- R1   [ -1   -3   13   ]
                   2       [                ]
   
                   -3      [                ]  
       R3 := R3 - --- R2   [  2   -3    4   ]
                   1       [                ]
      -------------------> [  2   -1    5   ]
                           [                ]
                           [ -1   +3   -2   ]
                           [                ]
   
         [  1   0   0  ]       [  2  -3   4  ]
     L = [  2   1   0  ]   U = [  0  -1   5  ]
         [ -1   3   1  ]       [  0   0  -2  ]
   

2. Use the L and U to compute the determinant of A.

   Answer:

      det(A) = det(L*U)
             = det(L)*det(U)
             = 1 * 2 * (-1) * (-2)
             = 4