# January 18, 2002.   Dr. W. J. Martin
# Sample MAPLE input file.  Matrix computations.
#
# GOAL:  Solve the linear system  
#                        x1 - 2x2       = -5
#                       2x1 +  x2 +  x3 =  5
#                             3x2 - 2x3 = -4
#        using Cramer's Rule and directly.
#
#

with(linalg);   # Load MAPLE's suite of linear algebra routines.

M := matrix
     (3,4,    # Matrix M has 3 rows, 4 columns. Here are teh entries:
      [ 1, -2,  0, -5,
        2,  1,  1,  5,
        0,  3, -2, -4]
     );


# Obtain the coefficient matrix:

A := submatrix( M, 1..3, 1..3);   # Select first, second, third column of M

multiply(  inverse(A),  M);

# So our solution is x = [ -1,  2,  5 ]^T

# Cramer's rule. (Only works if det(A) <> 0.) 
print(` Computing the determinant of A:`);
det(A);


# In Cramer's rule, to find xi: 
#      (1)  replace the i-th column of A by the RHS 
#                      vector b = [ -5,  5,  -4 ]^T,
#      (2)  compute the determinant of this matrix,
#      (3)  divide this answer by det(A) to find xi.

# Solve for x1 using Cramer's Rule:
B1 := submatrix( M, 1..3, [4,2,3]);
printf(` Determinant of B1 is %g \n`,det(B1));

X1 := det(B1)/det(A);
       
# Solve for x2 using Cramer's Rule:
B2 := submatrix( M, 1..3, [1,4,3]);
printf(` Determinant of B2 is %g \n`,det(B2));

X2 := det(B2)/det(A);
       
# Solve for x3 using Cramer's Rule:
B3 := submatrix( M, 1..3, [1,2,4]);
printf(` Determinant of B3 is %g \n`,det(B3));

X3 := det(B3)/det(A);
       
       


quit