1,2500
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1,2500 | -2,5000 | 1,2500 | -0,7500 | 1,0000 | 0,0000 | 0,0000 | ||
0,0000 | 0,7500 | 2,5000 | 3,7500 | -0,2500 | 0,0000 | 1,0000 | 0,0000 | ||
0,0000 | 6,0000 | 2,0000 | 7,0000 | 0,0000 | 0,0000 | 0,0000 | 1,0000 |
2. A 12: H 12 A 7: H 7:
A 12: H 12, =A7:H7 Ctrl Shift, Enter (Ctrl + Shift + Enter).
B 13 =B8/$B8; B 13 H 13.
B 14 =B9-B$13*$B9; B 14 H 14.
B 14: H 14 H 15.
A 12: H 15 :
1,0000 | 1,2500 | 0,5000 | 0,2500 | 0,2500 | 0,0000 | 0 | 0 |
0,0000 | 1,0000 | -2,0000 | 1,0000 | -0,6000 | 0,8000 | 0,0000 | 0,0000 |
| 0,0000 |
4,0000 | 3,0000 | 0,2000 | -0,6000 | 1,0000 | 0,0000 |
| 0,0000 | 14,0000 | 1,0000 | 3,6000 | -4,8000 | 0,0000 | 1,0000 |
3. A 12: H 15 A 17: H 18, A 12: H 15, =A12:H13 Ctrl Shift , Enter.
C 19 =C14/$C14; C 19 H 19.
C 20 =C15-C$19*$C15, C 20 H 20. A 17: H 20 :
1,0000 | 1,2500 | 0,5000 | 0,2500 | 0,2500 | 0,0000 | 0 | 0 |
0,0000 | 1,0000 | -2,0000 | 1,0000 | -0,6000 | 0,8000 | 0 | 0 |
|
| 1,0000 | 0,7500 | 0,0500 | -0,1500 | 0,2500 | 0,0000 |
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| 0,0000 |
-9,5000 | 2,9000 | -2,7000 | -3,5000 | 1,0000 |
4. . A 22: H 25 , .
A 22: H 24 =A17:H19 , Ctrl Shift, Enter. D 25 =D20/$D20, D 25 H 25. A 22: H 25 :
1,0000 | 1,2500 | 0,5000 | 0,2500 | 0,2500 | 0,0000 | 0 | 0 |
0,0000 | 1,0000 | -2,0000 | 1,0000 | -0,6000 | 0,8000 | 0 | 0 |
0,0000 | 0,0000 | 1,0000 | 0,7500 | 0,0500 | -0,1500 | 0,25 | 0 |
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| 1,0000 | -0,3053 | 0,2842 | 0,3684 | -0,1053 |
.
5. A 30: H 30, =A25:H25 Ctrl + Shift + Enter. D 29 =D24-D$25*$D24, D 29 H 29. D 29 A 29. A 29: H 29 27.
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6. A 34: H 35, =A29:H30 Ctrl + Shift + Enter. C 33 =C28-C$34*$C28, C 33 H 33. C 33 A 33. A 33: H 33 32.
7. A 38: H 40, =A33:H35 Ctrl + Shift + Enter. B 37 =B32-B$38*$B32, B 37 H 37. B 37 A 37.
A 37: D 40 , E 37: H 40 :
A | B | C | D | E | F | G | H | |
37 | 1 | 0 | 0 | 0 | -0,14211 | 0,373684 | 0,447368 | -0,34211 |
38 | 0 | 1 | 0 | 0 | 0,263158 | -0,21053 | -0,42105 | 0,263158 |
39 | 0 | 0 | 1 | 0 | 0,278947 | -0,36316 | -0,02632 | 0,078947 |
40 | 0 | 0 | 0 | 1 | -0,30526 | 0,284211 | 0,368421 | -0,10526 |
A 43: D 46, =(A2:D5;E37:H40) Ctrl + Shift + Enter. .
C ++ .
#include <except.h>
#include <iostream.h>
long double detA(long double **a, const int n);
int main(){
long double **a; long double dA; int i,j,n;
cout <<" input n = "; cin >> n;
try {
a= new long double*[n]; for(i=0;i<n;i++) a[i]=new long double[n];
}
catch (xalloc){cout <<"\nCould not allocate\n"; exit(-1);}
cout <<"\n input matrix a \n";
for (i=0; i<n; i++)for (j=0; j<n; j++)cin >> a[i][j];
dA = detA(a, n);
cout << "\n matrix a: ";
for (i=0; i<n; i++){cout << "\n"; for (j=0; j<n; j++) cout <<" "<< a[i][j];}
cout << "\n determinant A = "; cout << dA;
cout << "\n Press Key and Enter to continue";
cin >> i; // for pause
for(i=0;i<n;i++)delete[] a[i];
delete a;
return 0;
}//end main
long double detA(long double **a, const int n){
long double **aa;
int i, k, m, im; long double amm, aim, r,d;
try {aa= new long double*[n];
for(i=0;i<n;i++) aa[i]=new long double[n]; }
catch (xalloc){cout <<"\nCould not allocate\n"; exit(-1);}
for (i = 0; i <= n-1; i++)
for (k = 0; k <= n-1; k++) aa[i][k] = a[i][k];
d = 1;
for (m = 0; m <= n-2; m++) {// m
amm = aa[m][m]; im = m;
for (i = m; i <= n-1; i++)
if(aa[i][m] > amm){amm = aa[i][m]; im = i; } d = d*amm;
if(im!= m)d = - d;
cout <<"\n amm = "<<amm;
if(im!= m)for (k = m; k <= n-1; k++)
{r = aa[im][k]; aa[im][k] = aa[m][k]; aa[m][k] = r;}
for (k = m; k <= n-1; k++)aa[m][k] = aa[m][k]/amm; // 3.16
for (i = m + 1; i <= n-1; i++){// i
aim = aa[i][m];
for (k = m; k <= n-1; k++)
aa[i][k] = aa[i][k] - aa[m][k]*aim; // 3.17
}// end i
}// end m
d = d* aa[n-1][n-1]; cout <<"\n amm = "<< aa[n-1][n-1];
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for(i=0;i<n;i++)delete[] aa[i];
delete aa;
return d;
}// end detA
, a [][], - detA() aa [][]. , .
:
input n = 4
input matrix a
4 5 2 1 3 5 -1 2 1 2 3 4 0 6 2 7 [ ]
amm = 4
amm = 6
amm = 2.25
amm = 3.51852
matrix a:
4 5 2 1
3 5 -1 2
1 2 3 4
0 6 2 7
Determinant A = 190
Press key and Enter to continue
:
#include <except.h>
#include <iostream.h>
int Matr_inv(long double **a, long double **a1, const int n);
int main(){
long double **a; long double **ainv; int i,j,n;
cout <<" input n = "; cin >> n;
try {
ainv= new long double*[n]; for(i=0;i<n;i++) ainv[i]=new long double[n];
}
catch (xalloc){cout <<"\nCould not allocate\n"; exit(-1);}
try {
a= new long double*[n]; for(i=0;i<n;i++) a[i]=new long double[n];
}
catch (xalloc){cout <<"\nCould not allocate\n"; exit(-1);}
cout <<"\n input matrix a \n";
for (i=0; i<n; i++)for (j=0; j<n; j++)cin >> a[i][j];
cout << "\n matrix a: ";
for (i=0; i<n; i++){cout << "\n";
for (j=0; j<n; j++) cout <<" "<< a[i][j];}
Matr_inv(a, ainv, n);
cout << "\n ------------------- matr a: ";
for (i=0; i<n; i++){cout << "\n";
for (j=0; j<n; j++) cout <<" "<< a[i][j];}
cout << "\n -------------------- inv matr ainv: ";
for (i=0; i<n; i++){cout << "\n";
for (j=0; j<n; j++) cout <<" "<< ainv[i][j];}
cout << "\n Press Key and Enter to continue";
cin >> i; // for pause
for(i=0;i<n;i++)delete[] a[i];
delete a;
for(i=0;i<n;i++)delete[] ainv[i];
delete ainv;
return 0;
}//end main
int Matr_inv(long double **a, long double **a1, const int n){
int i, k, m, im; long double amm, aim, r;
for (i = 0; i <= n-1; i++)
for (k = 0; k <= n-1; k++){
if(i==k)a1[i][k] = 1; else a1[i][k] = 0;}
// 1.
for (m = 0; m <= n-2; m++) {// m
amm = a[m][m]; im = m;
for (i = m; i <= n-1; i++)
if(a[i][m] > amm){amm = a[i][m]; im = i; }
if(im!= m){
for (k = m; k <= n-1; k++){
r = a[im][k]; a[im][k] = a[m][k]; a[m][k] = r;}
for (k = 0; k <= n-1; k++){
r = a1[im][k]; a1[im][k] = a1[m][k]; a1[m][k] = r;}
}
for (k = m; k <= n-1; k++)a[m][k] = a[m][k]/amm;
for (k = 0; k <= n-1; k++) a1[m][k] = a1[m][k]/amm;
for (i = m + 1; i <= n-1; i++){// i
aim = a[i][m];
for (k = m; k <= n-1; k++)a[i][k] = a[i][k] - a[m][k]*aim;
for (k = 0; k <= n-1; k++)a1[i][k] = a1[i][k] - a1[m][k]*aim;
}// end i
}// end m
// 2.
amm = a[n-1][n-1]; a[n-1][n-1] = 1;
for (k = 0; k <= n-1; k++) a1[n-1][k] = a1[n-1][k]/amm;
for (m = n-1; m >= 0; m--){
for (i = m-1; i >= 0; i--){// i
aim = a[i][m]; a[i][m] = 0;
for (k = 0; k <= n-1; k++)a1[i][k] = a1[i][k] - a1[m][k]*aim;
}// end i
}// end m
return 0;
}// end Matr_inv
Matr_inv(a, a1, n) . a , a 1 . 3.8:
input n = 4
input matrix a
4 5 2 1 3 5 -1 2 1 2 3 4 0 6 2 7 [ ]
matrix a
4 5 2 1
3 5 -1 2
1 2 3 4
0 6 2 7
---------------------------- matr a
1 0 0 0
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0 1 0 0
0 0 1 0
0 0 0 0
---------------------------- inv matr ainv
-0,142105 0,373684 0,447368 -0,342105
0,263158 -0,210526 -0,421053 0,263158
0,278947 -0,363158 -0,0263158 0,0789474
-0,305263 0,284211 0,368421 -0,105263
Press Key and Enter to continue
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