#include "matrix.h"

int main(){


 Matrix A(3,4),B(3,4),C(4,2);

 int i,j;
 for( i=0; i<3; i++)
    for(j=0; j<4; j++){
       A(i,j)=i+j+2;
       B(i,j)=-2*(i+j+2);
    }
 A(2,3) +=1.; // make full rank

 cout << "The matrix A is \n"
      << A;

 A = 2.0*A;
 
 cout << "\nAfter doubling, it is \n" << A;

 cout << "\nWhen added to B it is \n" << A+B;

 for( i=0; i<4; i++)
    for(j=0; j<2; j++)
       C(i,j) = 1.;

 cout << "\nWhen multiplied by C it is\n" << A*C;

 cout << "\nThe Transpose of A is \n" << transpose(A);

 Matrix E(A*transpose(A)); // E = A * AT
 
 Matrix X(3,2);
 
 for(i=0; i<3; i++)
    for(j=0; j<2; j++)
       X(i,j) = i+1+3*(j+1);
 
 Matrix F(E*X);
 
 cout << "The answers should be \n" << X;
 cout << "The answers are \n" << solve(E,F);

}