Mathc matrices/a225

Application

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
void fun(void)
{
double d = 3;
double e = 4;
	
double a[R3*C3]  ={ d*2 + e*3,  2,  3,
                    d*4 + e*1,  4,  1,
                    d*2 + e*5,  2,  5};

double a2[R3*C3] ={ 2,  2,  3,
                    4,  4,  1,
                    2,  2,  5};
                   
double a3[R3*C3] ={ 3,  2,  3,
                    1,  4,  1,
                    5,  2,  5};                   
                                           
double **A  = ca_A_mR(a ,i_mR(R3,C3));
double **A2 = ca_A_mR(a2,i_mR(R3,C3));
double **A3 = ca_A_mR(a3,i_mR(R3,C3));

  clrscrn();
  printf(" If C1 a column of A is a linear combination  of\n"
         " one or several column of A, then we can write :\n\n\n"     
         "           |(d y1 + e z1)  y1  z1|              \n" 
         "  det(A) = |(d y2 + e z2)  y2  z2| =            \n" 
         "           |(d y3 + e z3)  y3  z3|              \n\n\n"
         "        |y1   y1  z1|     | z1  y1  z1|         \n" 
         "      d |y2   y2  z2| + e | z2  y2  z2|         \n" 
         "        |y3   y3  z3|     | z3  y3  z3|         \n\n\n"
         " Remark : If C1 == C2 then det(A) = 0           \n\n\n");
  stop();  
  
  clrscrn();
  printf(" With : d = %.0f; e = %.0f;  \n\n\n\n"
         " A  :               |(d C2 + e C3) C2 C3|",d,e);
  p_mR(A ,S3,P0,C6);

  printf(" A2 :               |C2 C2 C3|");
  p_mR(A2,S3,P0,C6);
  
  printf(" A3 :               |C3 C2 C3|");
  p_mR(A3,S3,P0,C6); 
  
  printf(" det_R(A)  = %+.0f ="   
         " d det_R(A2) + e det_R(A3)  = %+.0f\n\n\n"
          ,det_R(A), d*det_R(A2)+e*det_R(A3)); 
           
  stop();

  f_mR(A );
  f_mR(A2);
  f_mR(A3);  
}
/* ------------------------------------ */
int main(void)
{
  fun();

  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Exemple de sortie écran :

 ------------------------------------
 If C1 a column of A is a linear combination  of
 one or several column of A, then we can write :


           |(d y1 + e z1)  y1  z1|              
  det(A) = |(d y2 + e z2)  y2  z2| =            
           |(d y3 + e z3)  y3  z3|              


        |y1   y1  z1|     | z1  y1  z1|         
      d |y2   y2  z2| + e | z2  y2  z2|         
        |y3   y3  z3|     | z3  y3  z3|         


 Remark : If C1 == C2 then det(A) = 0           


 Press return to continue. 


 ------------------------------------
 With : d = 3; e = 4;  



 A  :               |(d C2 + e C3) C2 C3|
+18  +2  +3 
+16  +4  +1 
+26  +2  +5 

 A2 :               |C2 C2 C3|
 +2  +2  +3 
 +4  +4  +1 
 +2  +2  +5 

 A3 :               |C3 C2 C3|
 +3  +2  +3 
 +1  +4  +1 
 +5  +2  +5 

 det_R(A)  = -0 = d det_R(A2) + e det_R(A3)  = +0


 Press return to continue.