CRAMERS3.DOC

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CRAMERS3.COM IS AN S-BASIC PROGRAM USED TO FIND THE SOLUTION SET TO
3 LINEAR EQUATIONS IN 3 UNKNOWNS. IT MAKES USE OF CRAMER'S RULE FROM
ALGEBRA. IT WAS WRITTEN BY MIKE FINERTY 10/18/84 TO ALLEVIATE
FRUSTRATION ARISING IN THE WRITING OF ANOTHER PROGRAM. IT IS IN THE
PUBLIC DOMAIN FOR NON COMERCIAL USE  

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     DURING THE SUMMER OF 1984, I WROTE A CRAMER'S RULE PROGRAM
IN FORTRAN FOR A CLASS IN FORTRAN 77. THE PROGRAM MADE USE OF 4
SUBROUTINES AND TWO COMMON BLOCK STATEMENTS. LAST NIGHT IT
OCCURED TO ME THAT THERE WAS A SIMPLER SOLUTION USING ONE
SUBROUTINE AND ONE COMMON BLOCK. CRAMERS3.COM IS THE RESULT.

     THE PROGRAM REQUIRES THE INPUT OF 9 COEFFICIENTS AND 3
CONSTANTS AS THEY ARE READ IN A LINE OFF THE PAGE. THE GENERAL
FORM OF THE EQUATIONS IS:

     A(N)*X1 + B(N)*X2 + C(N)*X3 = D(N) ; N = {1,2,3}

     THE A'S, B'S AND C'S FORM A MATRIX AS FOLLOWS:

            | A(1)   B(1)   C(1) |
            |                    |
            | A(2)   B(2)   C(2) |  = MAT0
            |                    |
            | A(3)   B(3)   C(3) |

     THE DETERMINATE OF THE A,B&C'S IS CALLED DET0 AND IS
EVALUATED BY SUBROUTINE 100 (BOTTOM OF .PRN AND .BAS FILES).
    
     BY SUBSTITUTING D(N) FOR A(N),B(N) OR C(N) A NEW MATRIX IS
CREATED, WHICH CONFORMS TO THE REQUIREMENT OF CRAMER'S RULE.

     RESPECTIVELY: THE DETERMINATE SOLUTION TO THESE SINGLE
SUBSTITUTIONS ARE DET1, DET2, AND DET3, OBTAINED BY SENDING THE 
MATRIX FORMED BY X(N),Y(N) AND Z(N) TO THE DETERMINATE SOLVER,
SUBROUTINE 100. WHEN X(N) = D(N), DET1 IS RETURNED. WHEN Y(N) =
D(N), DET2 IS RETURNED AND WHEN Z(N) = D(N), DET3 IS RETURNED.
THESE ARE RETURNED IN THE FORM OF THE VARIABLE "DET" AND ALL FOUR
DETERMINATE SOULUTIONS ARE STORED IN THE HOLDING VARIABLES DET0,
DET1, DET2 AND DET3, RESPECTIVELY.

     THE SOLUTION SET IS GIVEN BY THE FOLLOWING RELATIONS:

                   X1 = DET1/DET0
                   X2 = DET2/DET0
                   X3 = DET3/DET0

THESE ARE RETURNED AS DOUBLE PRECISSION VALUES BY THE PROGRAM.

     THE PROGRAM HAS BEEN CHECKED OUT BY SOLVING THE PROBLEM SET
IN SECTION 46 OF BRINK'S @U(A FIRST YEAR OF COLLEGE MATHEMATICS)
FROM WHICH THE ALGORITHM WAS TAKEN.

     I HOPE THE PROGRAM IS OF USE TO STUDENTS CHECKING THEIR
HOMEWORK BY COMPUTER, & OTHERS WHO NEED THE SOLUTION AND ARE NOT
PARTICUALARLY INTERESTED IN THE METHOD (MORE GENERAL TYPES OF
SOLUTIONS EXIST USING INVERSE MATRICIES). I ADVISE STUDENTS WHO
ARE STUDYING LINEAR EQUATIONS IN 3 UNKNOWNS TO DO THE PROBLEM OUT
BY HAND FIRST. I GUARANTEE THAT YOU WILL NOT BE EXAMINED ON MY
ABILITY TO PROGRAM A COMPUTER. USE IT TO CHECK YOUR HOMEWORK; BUT
DO THAT HOMEWORK TOO.

         			MIKE FINERTY
 				2358 E PARKSIDE DR
				TUCSON, ARIZONA 85713