Macierz X

Macierz L

12.3630

-5.5779

8.9407

-7.3419

x

19.8705

-5.5779

6.7203

-3.2827

7.4363 *

y

=

-0.3768

8.9407

-3.2827

15.9215

-4.0138

t

31.4851

-7.3419

7.4363

-4.0138

11.3984

z

2.2257

12.363

-5.5779

8.9407

-7.3419

12.3630

0.0000

0.0000

0.0000

1.0000

-0.4512

0.7232

-0.5939

-5.5779

6.7203

-3.2827

7.4363 =

-5.5779

4.2037

0.0000

0.0000

*

0.0000

1.0000

0.1787

0.9810

8.9407

-3.2827

15.9215

-4.0138

8.9407

0.7511

9.3215

0.0000

0.0000

0.0000

1.0000

0.0600

-7.3419

7.4363

-4.0138

11.3984

-7.3419

4.1238

0.5589

2.9594

0.0000

0.0000

0.0000

1.0000

Macierz E

12.3630

0.0000

0.0000

0.0000

0.081

0.000

0.000

0.000

1

0

0

0

-5.5779

4.2037

0.0000

0.0000 *

0.107

0.238

0.000

0.000 =

0

1

0

0

8.9407

0.7511

9.3215

0.0000

-0.086

-0.019

0.107

0.000

0

0

1

0

-7.3419

4.1238

0.5589

2.9594

0.067

-0.328

-0.020

0.338

0

0

0

1

1.0000

-0.4512

0.7232

-0.5939

1.0000

0.4512

-0.8038

0.1994

1

0

0

0

0.0000

1.0000

0.1787

0.9810 *

0.0000

1.0000

-0.1787

-0.9703 =

0

1

0

0

0.0000

0.0000

1.0000

0.0600

0.0000

0.0000

1.0000

-0.0600

0

0

1

0

0.0000

0.0000

0.0000

1.0000

0.0000

0.0000

0.0000

1.0000

0

0

0

1

1.0000

0.4512

-0.8038

0.1994

0.0809

0.0000

0.0000

0.0000

0.2121

0.0573

-0.0903

0.0674

0.0000

1.0000

-0.1787

-0.9703

0.1073

0.2379

0.0000

0.0000

0.0573

0.5594

0.0005

-0.3279

0.0000

0.0000

1.0000

-0.0600 *

-0.0862

-0.0192

0.1073

0.0000 =

-0.0903

0.0005

0.1085

-0.0203

0.0000

0.0000

0.0000

1.0000

0.0674

-0.3279

-0.0203

0.3379

0.0674

-0.3279

-0.0203

0.3379

Macierz X

Macierz L

1.5000

0.2121

0.0573

-0.0903

0.0674

19.8705

0.2143 =

0.0573

0.5594

0.0005

-0.3279

*

-0.3768

1.5769

-0.0903

0.0005

0.1085

-0.0203

31.4851

1.5769

0.0674

-0.3279

-0.0203

0.3379

2.2257

Macierz X

Macierz L

12.3630

-5.5779

8.9407

-7.3419

1.5000

19.8705

-5.5779

6.7203

-3.2827

7.4363 *

0.2143

=

-0.3768

8.9407

-3.2827

15.9215

-4.0138

1.5769

31.4851

-7.3419

7.4363

-4.0138

11.3984

1.5769

2.2257

Kraków
Ruchel Jan

7.3419 x + 7.4363 y + 4.0138 t + 11.3984 z = + 2.2257

Obliczenie przy wykorzystaniu rozkładu A = H

T

* G

11 lipiec 2010

Układ czterech równań liniowych

12.363 x - 5.5779 y + 8.9407 t - 7.3419 z = + 19.8705
- 5.5779 x + 6.7203 y - 3.2827 t + 7.4363 z = - 0.3768
8.9407 x - 3.2827 y + 15.9215 t - 4.0138 z = + 31.4851

Macierz G

Macierz G

-1

Macierz E

Układ równań

Macierz A

Rozkład

Macierz A

Macierz H

T

Macierz G

Kontrola

Macierz A

Odwrotność macierzy współczynników

Macierz G

-1

Macierz (H

T

)

-1

Macierz A

-1

Rozwiązanie

Macierz A

-1

Odwrotność H

T

Macierz H

T

Macierz (H

T

)

-1

Odwrotność G

12.363 x - 5.5779 y + 8.9407 t - 7.3419 z = + 19.8705
- 5.5779 x + 6.7203 y - 3.2827 t + 7.4363 z = - 0.3768
8.9407 x - 3.2827 y + 15.9215 t - 4.0138 z = + 31.4851
7.3419 x + 7.4363 y + 4.0138 t + 11.3984 z = + 2.2257

Macierz X

12.3630

-5.5779

8.9407

-7.3419

x

-5.5779

6.7203

-3.2827

7.4363

*

y

=

8.9407

-3.2827

15.9215

-4.0138

t

-7.3419

7.4363

-4.0138

11.3984

z

12.3630

-5.5779

8.9407

-7.3419

3.5161

0

0

0

3.5161

-1.5864

2.5428

-2.0881

-5.5779

6.7203

-3.2827

7.4363

=

-1.5864 2.050288

0

0

*

0.0000

2.0503

0.3664

2.0113

8.9407

-3.2827

15.9215

-4.0138

2.5428 0.366357 3.053118

0

0.0000

0.0000

3.0531

0.1830

-7.3419

7.4363

-4.0138

11.3984

-2.0881 2.011329 0.183048 1.720285

0.0000

0.0000

0.0000

1.7203

3.5161

0.0000

0.0000

0.0000

0.2844

0.0000

0.0000

0.0000

1

0

0

0

-1.5864

2.0503

0.0000

0.0000

*

0.2201

0.4877

0.0000

0.0000

=

0

1

0

0

2.5428

0.3664

3.0531

0.0000

-0.2633

-0.0585

0.3275

0.0000

0

0

1

0

-2.0881

2.0113

0.1830

1.7203

0.1159

-0.5640

-0.0349

0.5813

0

0

0

1

0.2844

0.0000

0.0000

0.0000

0.2844

0.2201

-0.2633

0.1159

0.2201

0.4877

0.0000

0.0000

=

0.0000

0.4877

-0.0585

-0.5640

-0.2633

-0.0585

0.3275

0.0000

0.0000

0.0000

0.3275

-0.0349

0.1159

-0.5640

-0.0349

0.5813

0.0000

0.0000

0.0000

0.5813

0.2844

0.2201

-0.2633

0.1159

0.2844

0.0000

0.0000

0.0000

0.2121

0.0573

-0.0903

0.0674

0.0000

0.4877

-0.0585

-0.5640

*

0.2201

0.4877

0.0000

0.0000

=

0.0573

0.5594

0.0005

-0.3279

0.0000

0.0000

0.3275

-0.0349

-0.2633

-0.0585

0.3275

0.0000

-0.0903

0.0005

0.1085

-0.0203

0.0000

0.0000

0.0000

0.5813

0.1159

-0.5640

-0.0349

0.5813

0.0674

-0.3279

-0.0203

0.3379

Macierz X

Macierz L

1.5000

0.2121

0.0573

-0.0903

0.0674

19.8705

0.2143

=

0.0573

0.5594

0.0005

-0.3279

*

-0.3768

1.5769

-0.0903

0.0005

0.1085

-0.0203

31.4851

1.5769

0.0674

-0.3279

-0.0203

0.3379

2.2257

Macierz X

Macierz L

12.3630

-5.5779

8.9407

-7.3419

1.5000

19.871

-5.5779

6.7203

-3.2827

7.4363

*

0.2143

=

-0.377

8.9407

-3.2827

15.9215

-4.0138

1.5769

31.485

-7.3419

7.4363

-4.0138

11.3984

1.5769

2.2257

Kraków
Ruchel Jan

19.8705

Układ czterech równań liniowych

Obliczenie przy wykorzystaniu rozkładu A = R

T

* R

Układ równań

Macierz A

Macierz L

-0.3768

31.4851

2.2257

Rozkład

Macierz A

Macierz R

T

Macierz R

Odwrotność pierwiastka

Macierz R

T

Macierz (R

T

)

-1

E

Kontrola

Macierz A

Transpoza

Macierz (R

T

)

-1

( (R

T

)

-1

)

T

= R

-1

11 lipiec 2010

Odwrotność macierzy współczynników

Macierz R

-1

Macierz (R

T

)

-1

Macierz A

-1

Rozwiązanie

Macierz A

-1