Mathc matrices/a225
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c00a.c */
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.

Mathc matrices/a226
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c00a.c */
void fun(void)
double d = 3;
double a[R3*C3] = { 5, d*5 + 2, 3,
 3, d*3 + 4, 1,
 4, d*4 + 2, 5}; 
double a1[R3*C3] = { 5, + 2, 3,
 3, + 4, 1,
 4, + 2, 5}; 
double a2[R3*C3] ={ 5, 5, 3,
 3, 3, 1,
 4, 4, 5}; 
double **A = ca_A_mR(a ,i_mR(R3,C3));
double **A1 = ca_A_mR(a1,i_mR(R3,C3));
double **A2 = ca_A_mR(a2,i_mR(R3,C3));
 clrscrn();
 printf(" If C2 a column of A is a linear combination of\n"
 " (C2 + d*C1), then we can write : \n\n\n" 
 " | x1 (y1 + d*x1) z1| \n" 
 " det(A) = | x2 (y2 + d*x2) z1| = \n" 
 " | x3 (y3 + d*x3) z1| \n\n\n"
 " |x1 y1 z1| | x1 x1 z1| \n" 
 " |x2 y2 z2| + d | x2 x2 z2| \n" 
 " |x3 y3 z3| | x3 x3 z3| \n\n\n"
 " Remark : If C1 == C2 then det(A) = 0 \n\n\n");
 stop(); 
 clrscrn();
 printf(" With : d = %.0f; \n\n\n"
 " A |C1 (d C1 + C2) C3|",d);
 p_mR(A,S3,P0,C6);
 printf(" A1 : |C1 C2 C3)|");
 p_mR(A1,S3,P0,C6);
 printf(" A2 : |C1 C1 C3)|");
 p_mR(A2,S3,P0,C6);
 printf(" det_R(A) = %+.0f =" 
 " det_R(A1) + d*det_R(A2) = %+.0f\n\n\n",
 det_R(A), det_R(A1)+d*det_R(A2)); 
 stop();
 f_mR(A);
 f_mR(A1); 
 f_mR(A2); 
/* ------------------------------------ */
int main(void)
 fun();
 return 0;
/* ------------------------------------ */

Exemple de sortie écran :
 If C2 a column of A is a linear combination of
 (C2 + d*C1), then we can write : 
 | x1 (y1 + d*x1) z1| 
 det(A) = | x2 (y2 + d*x2) z1| = 
 | x3 (y3 + d*x3) z1| 
 |x1 y1 z1| | x1 x1 z1| 
 |x2 y2 z2| + d | x2 x2 z2| 
 |x3 y3 z3| | x3 x3 z3| 
 Remark : If C1 == C2 then det(A) = 0 
 Press return to continue. 
 ------------------------------------
 With : d = 3; 
 A |C1 (d C1 + C2) C3|
 +5 +17 +3 
 +3 +13 +1 
 +4 +14 +5 
 A1 : |C1 C2 C3)|
 +5 +2 +3 
 +3 +4 +1 
 +4 +2 +5 
 A2 : |C1 C1 C3)|
 +5 +5 +3 
 +3 +3 +1 
 +4 +4 +5 
 det_R(A) = +38 = det_R(A1) + d*det_R(A2) = +38
 Press return to continue.

Mathc matrices/a227
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c00a.c */
void fun(void)
double d1 = 5;
double d2 = 3;
double d3 = 4;
double a[R3*C3] = { 5, 5 + 2, 3,
 3, 3 + 4, 1,
 4, 4 + 2, 5}; 
double a1[R3*C3] = { 1, 5 + 2, 3,
 0, 3 + 4, 1,
 0, 4 + 2, 5}; 
double a2[R3*C3] = { 0, 5 + 2, 3,
 1, 3 + 4, 1,
 0, 4 + 2, 5}; 
double a3[R3*C3] = { 0, 5 + 2, 3,
 0, 3 + 4, 1,
 1, 4 + 2, 5}; 
double **A = ca_A_mR(a ,i_mR(R3,C3));
double **A1 = ca_A_mR(a1,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(" A : " 
 " det_R(A) = %+.0f",
 det_R(A));
 p_mR(A,S3,P0,C6);
 printf(" A1 : d1 = %.0f; " 
 " d1 det_R(A1) + d2 det_R(A2) + d3 det_R(A3) = %+.0f", 
 d1, d1*det_R(A1) + d2*det_R(A2) + d3*det_R(A3));
 p_mR(A1,S3,P0,C6);
 printf(" A2 : d2 = %.0f;", d2);
 p_mR(A2,S3,P0,C6);
 printf(" A3 : d3 = %.0f;", d3);
 p_mR(A3,S3,P0,C6); 
 stop();
 f_mR(A);
 f_mR(A1); 
 f_mR(A2); 
 f_mR(A3); 
/* ------------------------------------ */
int main(void)
 fun();
 return 0;
/* ------------------------------------ */

Exemple de sortie écran :
 A : det_R(A) = +38
 +5 +7 +3 
 +3 +7 +1 
 +4 +6 +5 
 A1 : d1 = 5; d1 det_R(A1) + d2 det_R(A2) + d3 det_R(A3) = +38
 +1 +7 +3 
 +0 +7 +1 
 +0 +6 +5 
 A2 : d2 = 3;
 +0 +7 +3 
 +1 +7 +1 
 +0 +6 +5 
 A3 : d3 = 4;
 +0 +7 +3 
 +0 +7 +1 
 +1 +6 +5 
 Press return to continue.

Mathc matrices/a228
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c00a.c */
void fun(void)
double a11 = 5;
double a21 = 3;
double a31 = 4;
double a[R3*C3] = { a11, 2, 3,
 a21, 4, 1,
 a31, 2, 5}; 
double **A = ca_A_mR(a ,i_mR(R3,C3));
 clrscrn();
 printf(" M = Minor; C = cofactor \n\n"
 " We work with the first column \n\n\n");
 printf(" A : det_R(A) = %+.0f", det_R(A));
 p_mR(A,S3,P0,C6);
 printf("\n"
 " det_R(A) = a11 M11 - a21 M21 + a31 M31 = %+.0f\n\n",
 + a11 * minor_R(A, R1, C1) 
 - a21 * minor_R(A, R2, C1) 
 + a31 * minor_R(A, R3, C1) ); 
 printf("\n"
 " det_R(A) = a11 C11 + a21 C21 + a31 C31 = %+.0f\n\n",
 + a11 * cofactor_R(A, R1, C1) 
 + a21 * cofactor_R(A, R2, C1) 
 + a31 * cofactor_R(A, R3, C1) ); 
 stop();
 f_mR(A); 
/* ------------------------------------ */
int main(void)
 fun();
 return 0;
/* ------------------------------------ */

Exemple de sortie écran :
 M = Minor; C = cofactor 
 We work with the first column 
 A : det_R(A) = +38
 +5 +2 +3 
 +3 +4 +1 
 +4 +2 +5 
 det_R(A) = a11 M11 - a21 M21 + a31 M31 = +38
 det_R(A) = a11 C11 + a21 C21 + a31 C31 = +38
 Press return to continue.

Mathc matrices/a229
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c00a.c */
void fun(void)
double a11 = 5;
double a12 = 2;
double a13 = 3;
double a[R3*C3] = { a11, a12, a13,
 3, 4, 1,
 4, 2, 5}; 
double **A = ca_A_mR(a ,i_mR(R3,C3));
 clrscrn();
 printf(" M = Minor; C = cofactor \n\n"
 " We work with the first row \n\n\n");
 printf(" A : det_R(A) = %+.0f", det_R(A));
 p_mR(A,S3,P0,C6);
 printf("\n"
 " det_R(A) = a11 M11 - a12 M12 + a13 M13 = %+.0f\n\n",
 + a11 * minor_R(A, R1, C1) 
 - a12 * minor_R(A, R1, C2) 
 + a13 * minor_R(A, R1, C3) ); 
 printf("\n"
 " det_R(A) = a11 C11 + a12 C12 + a13 C13 = %+.0f\n\n",
 + a11 * cofactor_R(A, R1, C1) 
 + a12 * cofactor_R(A, R1, C2) 
 + a13 * cofactor_R(A, R1, C3) ); 
 stop();
 f_mR(A); 
/* ------------------------------------ */
int main(void)
 fun();
 return 0;
/* ------------------------------------ */

Exemple de sortie écran :
 M = Minor; C = cofactor 
 We work with the first row 
 A : det_R(A) = +38
 +5 +2 +3 
 +3 +4 +1 
 +4 +2 +5 
 det_R(A) = a11 M11 - a12 M12 + a13 M13 = +38
 det_R(A) = a11 C11 + a12 C12 + a13 C13 = +38
 Press return to continue.