Assignment #6 - 84B

Assignment #6 - 84B


                            ASSIGNMENT 6
                                                     WEIGHT: 30
                                                     DUE: 20 NOVEMBER 84

     IN THIS ASSIGNMENT, YOU MUST FIRST WRITE A SIMPLE PASCAL PROCEDURE
TO COMPUTE THE DETERMINANT OF A 3X3 MATRIX M.  THE DETERMINANT OF M,
CALLED DET(M), IS DEFINED AS:
      __             __
      | A    A    A   |
      |  11   12   13 |
      |               |      --->  DET(M) = (A  A  A   + A  A  A
 M =  | A    A    A   |                       11 22 33    12 23 31
      |  21   22   23 |                            + A  A  A   )
      |               |                               13 21 32
      | A    A    A   |                       -   (A  A  A   + A  A  A
      |  31   32   33 |                             13 22 31    12 21 33
      --             --                                 + A  A  A   )
                                                           11 32 23

     IF THE DETERMINANT IS 0, THEN M IS SINGULAR.  THEREFORE, YOUR
PROCEDURE SHOULD RETURN A FLAG CALLED "SINGULAR" THAT IS TRUE IF THIS
CONDITION EXISTS AND FALSE OTHERWISE.

      TYPE MATRIX = ARRAY(3,3) OF INTEGER;
             .                 .
             .                 .
             .                 .
      PROCEDURE   FIND_DET(M:MATRIX; VAR SINGULAR:BOOLEAN;
                           VAR DET:INTEGER)  ;


     THEN, USE THE PRECEDING PROCEDURE TO FIND THE SOLUTION TO THE 3X3
SYSTEM OF EQUATIONS :

   A  X  + A  X  + A  X  = B
    11 1    12 2    13 3    1

   A  X  + A  X  + A  X  = B
    21 1    22 2    23 3    2

   A  X  + A  X  + A  X  = B
    31 1    32 2    33 3    3

USING CRAMER'S RULE.


     CRAMER'S RULE STATES THAT THE SOLUTION TO THE PRECEDING PROBLEM CAN
BE FOUND BY BUILDING AN "AUGMENTED MATRIX" M(I) BY REPLACING THE ITH
COLUMN OF M WITH THE CONSTANTS B , B  , B  .
                                1   2    3


THE VALUE OF X  AT THE SOLUTION POINT IS SIMPLY
              I

                         DET( M(I) )
                 X   =   -----------
                  I        DET( M )


FOR EXAMPLE, THE VALUE OF X  IS
                           1

                   __           __
                   |  B  A   A   |
                   |   1  12  13 |
                   |             |
                   |  B  A   A   |
             DET   |   2  22  23 |
                   |             |
                   |  B  A   A   |
                   |   3  32  33 |
                   --           --
   X   =  _________________________________
    1              __           __
                   | A   A   A   |
                   |  11  12  13 |
                   |             |
                   | A   A   A   |
             DET   |  21  22  23 |
                   |             |
                   | A   A   A   |
                   |  31  32  33 |
                   --           --

NOTE THAT THIS PROCEDURE WORKS ONLY IF THE MATRIX M IS NOT SINGULAR.
IF THIS CONDITION IS NOT MET, THEN YOU SHOULD PRINT A MESSAGE SPECIFYING
THAT THE GIVEN SYSTEM OF LINEAR EQUATIONS CANNOT BE SOLVED USING
CRAMER'S RULE.

     TEST YOUR PROGRAM WITH THE FOLLOWING 3 SYSTEMS OF LINEAR EQUATIONS:

     A    A    A    B
      K1   K2   K3   K
     _________________
     1    1    2    9
     2    4   -3    1
     3    6   -5    0


     2    1    3    0
     1    2    0    0
     0    1    1    0


     1   -2    7    4
     3    5    1    2
     4    3    8   -1