Exemple de sortie écran :
 A :
 +9 -2 +1 
-27 +6 -3 
+18 -4 +2 
 b :
 +3 +1 +2 
 +0 +0 +3 
 +1 +2 +0 
 Ab :
 +9 -2 +1 +3 +1 +2 
-27 +6 -3 +0 +0 +3 
+18 -4 +2 +1 +2 +0 
 ------------------------------------ 
 Copy/Past into the octave window.
 Ab=[
+9,-2,+1,+3,+1,+2;
-27,+6,-3,+0,+0,+3;
+18,-4,+2,+1,+2,+0]
 rref(Ab.00000000001)
 gj_PP_mR(Ab,YES) :
 +1.0000 -0.2222 +0.1111 -0.0000 -0.0000 -0.1111 
 +0.0000 +0.0000 +0.0000 +3.0000 +1.0000 +3.0000 
 +0.0000 +0.0000 +0.0000 +1.0000 +2.0000 +2.0000 
 Press return to continue. 
Les deux dernières lignes donnent :
 +0.0000 +0.0000 +0.0000 +3.0000 +1.0000 +3.0000 
 +0.0000 +0.0000 +0.0000 +1.0000 +2.0000 +2.0000 
 ou bien
 +0.0000 = +3.0000 +1.0000 +3.0000 
 +0.0000 = +1.0000 +2.0000 +2.0000 
 en introduisant B et C
 +0.0000 = +3.0000 B +1.0000 C +3.0000 
 +0.0000 = +1.0000 B +2.0000 C +2.0000 
 soit le système 
 3.0000 B +1.0000 C = -3.0000 
 +1.0000 B +2.0000 C = -2.0000
 cela donne
 B = -4./5. 
 C = -3./5.

Mathc matrices/a47
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00.c */
/* ------------------------------------ */
/* ------------------------------------ */
//#define B (+2./5.)
//#define C (-6./5.)
/* ------------------------------------ */
int main(void)
/* 
 * Find a value for "B" so that the system is compatible.
double ab[RA*(CA+Cb)]={
// A = x*B + y*C + z
 -7, +7, +9, -2, +4*B, +1*C, +1,
 -5, -6, -1, -8, +2*B, +3*C, +2,
 -21, +21, +27, -6, +3*B, +0*C, +3, 
 -14, +14, +18, -4, +0*B, +1*C, +4, 
double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(RA,CA,Cb));
double **A = c_Ab_A_mR(Ab,i_mR(RA,CA));
double **b = c_Ab_b_mR(Ab,i_mR(RA,Cb));
 clrscrn();
 printf(" A :");
 p_mR(A,S3,P0,C7);
 printf(" b :");
 p_mR(b,S3,P0,C7);
 printf(" Ab :");
 p_mR(Ab,S3,P0,C7);
 getchar();
 clrscrn();
 printf(" Copy/Past into the octave window.\n\n");
 p_Octave_mR(Ab,"Ab",P0);
 printf("\n rref(Ab.00000000001)\n\n");
 printf(" gj_PP_mR(Ab,YES) :");
 gj_PP_mR(Ab,YES);
 p_mR(Ab,S8,P4,C7);
 stop();
 f_mR(Ab);
 f_mR(b);
 f_mR(A);
 return 0;
/* ------------------------------------ */
 Calculer la valeur de B et de C pour que le système soit compatible.

Exemple de sortie écran :
 A :
 -7 +7 +9 -2 
 -5 -6 -1 -8 
-21 +21 +27 -6 
-14 +14 +18 -4 
 b :
 +4 +1 +1 
 +2 +3 +2 
 +3 +0 +3 
 +0 +1 +4 
 Ab :
 -7 +7 +9 -2 +4 +1 +1 
 -5 -6 -1 -8 +2 +3 +2 
-21 +21 +27 -6 +3 +0 +3 
-14 +14 +18 -4 +0 +1 +4 
 Copy/Past into the octave window.
 Ab=[
-7,+7,+9,-2,+4,+1,+1;
-5,-6,-1,-8,+2,+3,+2;
-21,+21,+27,-6,+3,+0,+3;
-14,+14,+18,-4,+0,+1,+4]
 rref(Ab.00000000001)
 gj_PP_mR(Ab,YES) :
 +1.0000 +0.0000 -0.6104 +0.8831 -0.2597 -0.2727 -0.2597 
 -0.0000 +1.0000 +0.6753 +0.5974 -0.1169 -0.2727 -0.1169 
 +0.0000 +0.0000 +0.0000 +0.0000 +3.0000 +1.0000 +0.0000 
 +0.0000 +0.0000 +0.0000 +0.0000 -2.0000 +1.0000 +2.0000 
 Press return to continue. 
Les deux dernières lignes donnent :
 +0.0000 +0.0000 +0.0000 +0.0000 +3.0000 +1.0000 +0.0000 
 +0.0000 +0.0000 +0.0000 +0.0000 -2.0000 +1.0000 +2.0000 
 ou bien
 +0.0000 = +3.0000 +1.0000 +0.0000 
 +0.0000 = -2.0000 +1.0000 +2.0000 
 en introduisant B et C
 +0.0000 = +3.0000 B +1.0000 C +0.0000 
 +0.0000 = -2.0000 B +1.0000 C +2.0000 
 soit le système 
 +3.0000 B +1.0000 C = -0.0000 
 -2.0000 B +1.0000 C = -2.0000 
 cela donne
 B = +2./5. 
 C = -6./5.

Mathc matrices/a48
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* ------------------------------------ */
/* Save as : c00.c */
/* ------------------------------------ */
/* ------------------------------------ */
//#define B (+0./1.)
//#define C (-1./2.)
/* ------------------------------------ */
int main(void)
/* 
 * Find a value for "B" so that the system is compatible.
double ab[RA*(CA+Cb)]={
// A = x*B + y*C + z
 +3, +9, +1, -1, -2, +2*B, +2*C, +2,
 +6, +18, +2, -2, -4, +0*B, +4*C, +4, 
 -4, +6, -2, +4, +9, +8*B, +0*C, +6, 
 -6, -6, +8, +1, +5, +0*B, +6*C, +3, 
 +9, +27, +3, -3, -6, -6*B, +0*C, +3,
double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(RA,CA,Cb));
double **A = c_Ab_A_mR(Ab,i_mR(RA,CA));
double **b = c_Ab_b_mR(Ab,i_mR(RA,Cb));
 clrscrn();
 printf(" A :");
 p_mR(A,S3,P0,C8);
 printf(" b :");
 p_mR(b,S3,P0,C8);;
 printf(" Ab :");
 p_mR(Ab,S3,P0,C8);
 getchar();
 clrscrn();
 printf(" Copy/Past into the octave window.\n\n");
 p_Octave_mR(Ab,"Ab",P0);
 printf("\n rref(Ab.00000000001)\n\n");
 printf(" gj_PP_mR(Ab,YES) :");
 gj_PP_mR(Ab,YES);
 p_mR(Ab,S8,P4,C8);
 stop();
 f_mR(Ab);
 f_mR(b);
 f_mR(A);
 return 0;
/* ------------------------------------ */
 Calculer la valeur de B et de C pour que le système soit compatible.

Exemple de sortie écran :
 A :
 +3 +9 +1 -1 -2 
 +6 +18 +2 -2 -4 
 -4 +6 -2 +4 +9 
 -6 -6 +8 +1 +5 
 +9 +27 +3 -3 -6 
 b :
 +2 +2 +2 
 +0 +4 +4 
 +8 +0 +6 
 +0 +6 +3 
 -6 +0 +3 
 Ab :
 +3 +9 +1 -1 -2 +2 +2 +2 
 +6 +18 +2 -2 -4 +0 +4 +4 
 -4 +6 -2 +4 +9 +8 +0 +6 
 -6 -6 +8 +1 +5 +0 +6 +3 
 +9 +27 +3 -3 -6 -6 +0 +3 
 ------------------------------------ 
 Copy/Past into the octave window.
 Ab=[
+3,+9,+1,-1,-2,+2,+2,+2;
+6,+18,+2,-2,-4,+0,+4,+4;
-4,+6,-2,+4,+9,+8,+0,+6;
-6,-6,+8,+1,+5,+0,+6,+3;
+9,+27,+3,-3,-6,-6,+0,+3]
 rref(Ab.00000000001)
 gj_PP_mR(Ab,YES) :
 +1.0000 +0.0000 +0.0000 -0.6596 -1.5851 -1.2340 -0.2553 -0.8936 
 +0.0000 +1.0000 +0.0000 +0.1383 +0.3404 +0.2695 +0.0213 +0.4078 
 +0.0000 +0.0000 +1.0000 -0.2660 -0.3085 -0.7234 +0.5745 +0.0106 
 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +4.0000 +4.0000 +2.0000 
 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +4.0000 +2.0000 +1.0000 
 Press return to continue. 
Les deux dernières lignes donnent :
 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +4.0000 +4.0000 +2.0000 
 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +4.0000 +2.0000 +1.0000 
 ou bien
 +0.0000 = +4.0000 +4.0000 +2.0000 
 +0.0000 = +4.0000 +2.0000 +1.0000 
 en introduisant B et C
 +0.0000 = +4.0000 B +4.0000 C +2.0000 
 +0.0000 = +4.0000 B +2.0000 C +1.0000 
 soit le système 
 +4.0000 B +4.0000 C = -2.0000 
 +4.0000 B +2.0000 C = -1.0000 
 cela donne
 B = (+0./1.)
 C = (-1./2.)

Mathc complexes/a157
Application
Calculer la valeur de B pour que le système soit compatible.
Calculer la valeur de B et de C pour que le système soit compatible.
Créer une matrice pour ce travail.