Resolver Sistemas de Ecuaciones Lineales Online

24/3/2015 Resolversistemasdeecuacioneslinealesonline

http://matrixcalc.org/es/slu.html#solveusingGaussianelimination%28%7B%7D%29 1/37

Matrixcalculator

deutsch/english/espaol/franais/galego/italiano/portugus//

Operacionesconmatrices

SolucindeSistemasdeEcuacionesLineales

Calculadoradedeterminantes

Clculodevalorespropiosyvectorespropios

Teoranecesaria

Solucindesistemasdeecuacioneslineales

EstaaplicacinresuelveunossistemasdeecuacioneslinealesporelmtododeeliminacindeGauss ,pormtododelaMatrizInversa,porlaRegladeCramer .TambinustedpuedeanalizarlacompatibilidaddesistemasporTeorema_de_RouchFrobenius paradeterminarelnmerodesoluciones.Entrecoeficientesdetussistema,dejeloscamposenblancosilasvariablesnoparticipanenlaecuacin.

SolucinporelMtododeGauss

SolucinporelMtododeGaussJordan

SolucinporlaRegladeCramer

SolucinporelMtododelaMatrizInversa

Anlisisdeconsistencia

Mostrarnmerosdecimales limpiar

x 1+ x 2+ x 3+ x 4= x 1+ x 2+ x 3+ x 4= x 1+ x 2+ x 3+ x 4= x 1+ x 2+ x 3+ x 4=

celdas limpiar +

limpiar

limpiar

LasolucinporelmtododeGauss

(1)

Larespuesta:Lasolucingeneral:X=


(1)

Larespuesta:

http://matrixcalc.org/es/http://matrixcalc.org/es/http://matrixcalc.org/es/vectors.htmlhttp://matrixcalc.org/de/slu.htmlhttp://es.wikipedia.org/wiki/Eliminaci%C3%B3n_de_Gauss-Jordanhttp://matrixcalc.org/it/slu.htmlhttp://matrixcalc.org/slu.htmlhttp://matrixcalc.org/pt/slu.htmlhttp://es.wikipedia.org/wiki/Teorema_de_Rouch%C3%A9%E2%80%93Frobeniushttp://matrixcalc.org/es/slu.htmlhttp://matrixcalc.org/es/slu.htmlhttp://es.wikipedia.org/wiki/Matriz_(matem%C3%A1ticas)http://es.wikipedia.org/wiki/Regla_de_Cramerhttp://matrixcalc.org/bg/slu.htmlhttp://matrixcalc.org/en/slu.htmlhttp://matrixcalc.org/fr/slu.htmlhttp://matrixcalc.org/gl/slu.htmlhttp://es.wikipedia.org/wiki/Sistema_de_ecuaciones_linealeshttp://matrixcalc.org/es/det.html



limpiar

limpiar

limpiar

limpiar

limpiar

limpiar

Lasolucingeneral:X=


(1)



(1)



(1)



(1)



(1)



(1)




limpiar

limpiar


(1)


LasolucinporelmtododeGaussJordan

~

~ ~

~

~

~

~

10 20 30 220030 0 20 190015 50 10 195020 15 30 255020 15 10 1400

110 1 2 3 22030 0 20 1900

15 50 10 195020 15 30 255020 15 10 1400

30

1 2 3 2200 60 70 470015 50 10 195020 15 30 255020 15 10 1400

15

1 2 3 2200 60 70 47000 20 35 135020 15 30 255020 15 10 1400

20

1 2 3 2200 60 70 47000 20 35 13500 25 30 185020 15 10 1400

20

1 2 3 2200 60 70 47000 20 35 13500 25 30 18500 25 50 3000

160

1 2 3 2200 1 7

62353

0 20 35 13500 25 30 18500 25 50 3000

20



limpiar

~

~

~

~

(1)

Noexistesolucin.


~

1 2 3 2200 1 7

62353

0 0 1753

87503

0 25 30 18500 25 50 3000

25

1 2 3 2200 1 7

62353

0 0 1753

87503

0 0 56

3253

0 25 50 3000

25

1 2 3 2200 1 7

62353

0 0 1753

87503

0 0 56

3253

0 0 1256

31253

3175

1 2 3 2200 1 7

62353

0 0 1 500 0 5

63253

0 0 1256

31253

56

1 0 0 00 1 0 00 0 1 00 0 0 10 0 0 0

x 1 = 0x 2 = 0

x 3 = 00 = 1

10 20 30 220030 0 20 190015 50 10 195020 15 30 255020 15 10 1400

3



~

~

~

~

~

~

~

10 20 30 22000 60 70 470015 50 10 195020 15 30 255020 15 10 1400

32

10 20 30 22000 60 70 47000 20 35 135020 15 30 255020 15 10 1400

2

10 20 30 22000 60 70 47000 20 35 13500 25 30 185020 15 10 1400

2

10 20 30 22000 60 70 47000 20 35 13500 25 30 18500 25 50 3000

13

10 20 30 22000 60 70 47000 0 175

38750

30 25 30 18500 25 50 3000

512

10 20 30 22000 60 70 47000 0 175

38750

3

0 0 56

3253

0 25 50 3000

512

10 20 30 22000 60 70 47000 0 175

38750

3

0 0 56

3253

0 0 1256

31253

170

10 20 30 22000 60 70 47000 0 175

38750

30 0 0 1500 0 0 0



limpiar

(1)

Noexistesolucin.


~

~ ~

~

~

~

~

10 x 1 +20 x 2 +30 x 3 = 220060 x 2 70 x 3 = 4700

1753

x 3 =8750

30 = 150

10 20 30 220030 0 20 190015 50 10 195020 15 30 255020 15 10 1400

110 1 2 3 22030 0 20 1900

15 50 10 195020 15 30 255020 15 10 1400

30

1 2 3 2200 60 70 470015 50 10 195020 15 30 255020 15 10 1400

15

1 2 3 2200 60 70 47000 20 35 135020 15 30 255020 15 10 1400

20

1 2 3 2200 60 70 47000 20 35 13500 25 30 185020 15 10 1400

20

1 2 3 2200 60 70 47000 20 35 13500 25 30 18500 25 50 3000

160

1 2 3 2200 1 7

62353

0 20 35 13500 25 30 18500 25 50 3000

20



limpiar

~

~

~

~

(1)

Noexistesolucin.


~ ~

1 2 3 2200 1 7

62353

0 0 1753

87503

0 25 30 18500 25 50 3000

25

1 2 3 2200 1 7

62353

0 0 1753

87503

0 0 56

3253

0 25 50 3000

25

1 2 3 2200 1 7

62353

0 0 1753

87503

0 0 56

3253

0 0 1256

31253

3175

1 2 3 2200 1 7

62353

0 0 1 500 0 5

63253

0 0 1256

31253

56

1 0 0 00 1 0 00 0 1 00 0 0 10 0 0 0

x 1 = 0x 2 = 0

x 3 = 00 = 1

1 4 6 202 8 1 202 4 3 204 6 2 503 5 4 50

2 1 4 6 200 0 11 202 4 3 204 6 2 503 5 4 50

2



~

~

~

~

~

~

~

(1)

Noexistesolucin.

1 4 6 200 0 11 200 4 9 204 6 2 503 5 4 50

4

1 4 6 200 0 11 200 4 9 200 10 22 303 5 4 50

3

1 4 6 200 0 11 200 4 9 200 10 22 300 7 14 10

+

1 4 6 200 4 20 400 4 9 200 10 22 300 7 14 10

1

1 4 6 200 4 20 400 0 11 200 10 22 300 7 14 10

52

1 4 6 200 4 20 400 0 11 200 0 28 700 7 14 10

74

1 4 6 200 4 20 400 0 11 200 0 28 700 0 21 60

2811

1 4 6 200 4 20 400 0 11 200 0 0 210

110 0 0 0

x 1 +4 x 2 +6 x 3 = 204 x 2 20 x 3 = 40

11 x 3 = 20

0 = 21011



limpiarLasolucinporelmtododeGaussJordan

~ ~

~

~

~ ~

~

~

~ ~

1 4 6 202 8 1 202 4 3 204 6 2 203 5 4 20

2 1 4 6 200 0 11 202 4 3 204 6 2 203 5 4 20

2

1 4 6 200 0 11 200 4 9 204 6 2 203 5 4 20

4

1 4 6 200 0 11 200 4 9 200 10 22 603 5 4 20

3

1 4 6 200 0 11 200 4 9 200 10 22 600 7 14 40

1 4 6 200 4 9 200 0 11 200 10 22 600 7 14 40

14

1 4 6 200 1 9

45

0 0 11 200 10 22 600 7 14 40

10

1 4 6 200 1 9

45

0 0 11 200 0 1

210

0 7 14 40

7

1 4 6 200 1 9

45

0 0 11 200 0 1

210

0 0 74

5

111

1 4 6 200 1 9

45

0 0 1 2011

0 0 12

10

0 0 74

5

12

1 0 0 00 1 0 00 0 1 00 0 0 10 0 0 0



limpiar

(1)

Noexistesolucin.


~ ~

~

~

~ ~

~

x 1 = 0x 2 = 0

x 3 = 00 = 1

1 4 6 252 8 1 322 4 3 324 6 2 423 5 4 30

2 1 4 6 250 0 11 182 4 3 324 6 2 423 5 4 30

2

1 4 6 250 0 11 180 4 9 184 6 2 423 5 4 30

4

1 4 6 250 0 11 180 4 9 180 10 22 583 5 4 30

3

1 4 6 250 0 11 180 4 9 180 10 22 580 7 14 45

1 4 6 250 4 9 180 0 11 180 10 22 580 7 14 45

14

1 4 6 250 1 9

492

0 0 11 180 10 22 580 7 14 45

10



limpiar

~

~ ~

(1)

Noexistesolucin.


~ ~

~

~

1 4 6 250 1 9

492

0 0 11 180 0 1

213

0 7 14 45

7

1 4 6 250 1 9

492

0 0 11 180 0 1

213

0 0 74

272

111

1 4 6 250 1 9

492

0 0 1 1811

0 0 12

13

0 0 74

272

12

1 0 0 00 1 0 00 0 1 00 0 0 10 0 0 0

x 1 = 0x 2 = 0

x 3 = 00 = 1

1 4 6 252 8 1 322 4 3 324 6 2 423 5 4 30

2 1 4 6 250 0 11 182 4 3 324 6 2 423 5 4 30

2

1 4 6 250 0 11 180 4 9 184 6 2 423 5 4 30

4

1 4 6 250 0 11 180 4 9 180 10 22 583 5 4 30

3



limpiar

~

~

~

~

~

(1)

Noexistesolucin.


~ ~

1 4 6 250 0 11 180 4 9 180 10 22 580 7 14 45

+

1 4 6 250 4 20 360 4 9 180 10 22 580 7 14 45

1

1 4 6 250 4 20 360 0 11 180 10 22 580 7 14 45

52

1 4 6 250 4 20 360 0 11 180 0 28 320 7 14 45

74

1 4 6 250 4 20 360 0 11 180 0 28 320 0 21 18

2811

1 4 6 250 4 20 360 0 11 180 0 0 152

110 0 0 0

x 1 +4 x 2 +6 x 3 = 254 x 2 20 x 3 = 36

11 x 3 = 18

0 = 15211

1 4 6 252 8 1 322 4 3 324 6 2 423 5 4 0

2 1 4 6 250 0 11 182 4 3 324 6 2 423 5 4 0

2



~

~

~ ~

~

~

~ ~

(1)

Noexistesolucin.

1 4 6 250 0 11 180 4 9 184 6 2 423 5 4 0

4

1 4 6 250 0 11 180 4 9 180 10 22 583 5 4 0

3

1 4 6 250 0 11 180 4 9 180 10 22 580 7 14 75

1 4 6 250 4 9 180 0 11 180 10 22 580 7 14 75

14

1 4 6 250 1 9

492

0 0 11 180 10 22 580 7 14 75

10

1 4 6 250 1 9

492

0 0 11 180 0 1

213

0 7 14 75

7

1 4 6 250 1 9

492

0 0 11 180 0 1

213

0 0 74

872

111

1 4 6 250 1 9

492

0 0 1 1811

0 0 12

13

0 0 74

872

12

1 0 0 00 1 0 00 0 1 00 0 0 10 0 0 0

x 1 = 0x 2 = 0

x 3 = 00 = 1



limpiarLasolucinporelmtododeGauss

~ ~

~

~

~

~

~

~

~

1 4 6 252 8 1 322 4 3 324 6 2 423 5 4 0

2 1 4 6 250 0 11 182 4 3 324 6 2 423 5 4 0

2

1 4 6 250 0 11 180 4 9 184 6 2 423 5 4 0

4

1 4 6 250 0 11 180 4 9 180 10 22 583 5 4 0

3

1 4 6 250 0 11 180 4 9 180 10 22 580 7 14 75

+

1 4 6 250 4 20 360 4 9 180 10 22 580 7 14 75

1

1 4 6 250 4 20 360 0 11 180 10 22 580 7 14 75

52

1 4 6 250 4 20 360 0 11 180 0 28 320 7 14 75

74

1 4 6 250 4 20 360 0 11 180 0 28 320 0 21 12

2811

1 4 6 250 4 20 360 0 11 180 0 0 152

110 0 0 0



limpiar

(1)

Noexistesolucin.


~ ~

~

~

~

x 1 +4 x 2 +6 x 3 = 254 x 2 20 x 3 = 36

11 x 3 = 18

0 = 15211

12 17 16 2529 14 11 2118 5 6 1895 15 19 28810 10 3 250

112

1 1712

43

21

9 14 11 2118 5 6 1895 15 19 28810 10 3 250

9

1 1712

43

21

0 54

1 22

8 5 6 1895 15 19 28810 10 3 250

8

1 1712

43

21

0 54

1 22

0 193

143

21

5 15 19 28810 10 3 250

5

1 1712

43

21

0 54

1 22

0 193

143

21

0 9512

373

183

10 10 3 250

10



~ ~

~

~

~

~

1 1712

43

21

0 54

1 22

0 193

143

21

0 9512

373

183

0 256

313

40

45

1 1712

43

21

0 1 45

885

0 193

143

21

0 9512

373

183

0 256

313

40

193

1 1712

43

21

0 1 45

885

0 0 14615

198715

0 9512

373

183

0 256

313

40

9512

1 1712

43

21

0 1 45

885

0 0 14615

198715

0 0 563

1313

0 256

313

40

256

1 1712

43

21

0 1 45

885

0 0 14615

198715

0 0 563

1313

0 0 413

3403

15146

1 1712

43

21

0 1 45

885

0 0 1 1987146

0 0 563

1313

0 0 413

3403

563

1 0 0 00 1 0 00 0 1 00 0 0 10 0 0 0



limpiar

(1)

Noexistesolucin.


~

~ ~

~

~

x 1 = 0x 2 = 0

x 3 = 00 = 1

12 17 16 2529 14 11 2018 5 6 1595 15 19 25810 10 3 210

34

12 17 16 2520 5

41 12

8 5 6 1595 15 19 25810 10 3 210

23

12 17 16 2520 5

41 12

0 193

143

9

5 15 19 25810 10 3 210

512

12 17 16 2520 5

41 12

0 193

143

9

0 9512

373

153

10 10 3 210

56

12 17 16 2520 5

41 12

0 193

143

9

0 9512

373

153

0 256

313

0

7615



limpiar

~

~

~

(1)

Noexistesolucin.


~ ~

12 17 16 2520 5

41 12

0 0 14615

2595

0 9512

373

153

0 256

313

0

193

12 17 16 2520 5

41 12

0 0 14615

2595

0 0 563

77

0 256

313

0

103

12 17 16 2520 5

41 12

0 0 14615

2595

0 0 563

77

0 0 413

40

14073

12 17 16 2520 5

41 12

0 0 14615

2595

0 0 0 1287373

0 0 0 0

12 x 1 +17 x 2 +16 x 3 = 25254 x 2 x 3 = 12

14615

x 3 =2595

0 = 1287373

12 17 16 2529 14 11 2018 5 6 1595 15 19 25810 10 3 210

112

1 1712

43

21

9 14 11 2018 5 6 1595 15 19 25810 10 3 210

9



~

~

~

~ ~

~

1 1712

43

21

0 54

1 12

8 5 6 1595 15 19 25810 10 3 210

8

1 1712

43

21

0 54

1 12

0 193

143

9

5 15 19 25810 10 3 210

5

1 1712

43

21

0 54

1 12

0 193

143

9

0 9512

373

153

10 10 3 210

10

1 1712

43

21

0 54

1 12

0 193

143

9

0 9512

373

153

0 256

313

0

45

1 1712

43

21

0 1 45

485

0 193

143

9

0 9512

373

153

0 256

313

0

193

1 1712

43

21

0 1 45

485

0 0 14615

2595

0 9512

373

153

0 256

313

0

9512



limpiar

~

~ ~

(1)

Noexistesolucin.


~ ~

~

1 1712

43

21

0 1 45

485

0 0 14615

2595

0 0 563

77

0 256

313

0

256

1 1712

43

21

0 1 45

485

0 0 14615

2595

0 0 563

77

0 0 413

40

15146

1 1712

43

21

0 1 45

485

0 0 1 777146

0 0 563

77

0 0 413

40

563

1 0 0 00 1 0 00 0 1 00 0 0 10 0 0 0

x 1 = 0x 2 = 0

x 3 = 00 = 1

12 17 16 2529 14 11 2018 5 6 1595 15 19 25812 10 5 210

112

1 1712

43

21

9 14 11 2018 5 6 1595 15 19 25812 10 5 210

9

1 1712

43

21

0 54

1 12

8 5 6 1595 15 19 25812 10 5 210

8



~

~

~

~

~

1 1712

43

21

0 54

1 12

0 193

143

9

5 15 19 25812 10 5 210

5

1 1712

43

21

0 54

1 12

0 193

143

9

0 9512

373

153

12 10 5 210

12

1 1712

43

21

0 54

1 12

0 193

143

9

0 9512

373

153

0 7 11 42

45

1 1712

43

21

0 1 45

485

0 193

143

9

0 9512

373

153

0 7 11 42

193

1 1712

43

21

0 1 45

485

0 0 14615

2595

0 9512

373

153

0 7 11 42

9512



limpiar

~

~ ~

(1)

Noexistesolucin.


~

~ ~

1 1712

43

21

0 1 45

485

0 0 14615

2595

0 0 563

77

0 7 11 42

7

1 1712

43

21

0 1 45

485

0 0 14615

2595

0 0 563

77

0 0 835

1265

15146

1 1712

43

21

0 1 45

485

0 0 1 777146

0 0 563

77

0 0 835

1265

563

1 0 0 00 1 0 00 0 1 00 0 0 10 0 0 0

x 1 = 0x 2 = 0

x 3 = 00 = 1

12 17 16 2529 14 11 2018 5 6 1595 15 19 25812 10 5 210

34

12 17 16 2520 5

41 12

8 5 6 1595 15 19 25812 10 5 210

23

12 17 16 2520 5

41 12

0 193

143

9

5 15 19 25812 10 5 210

512



~

~

~

~

~

(1)

12 17 16 2520 5

41 12

0 193

143

9

0 9512

373

153

12 10 5 210

1

12 17 16 2520 5

41 12

0 193

143

9

0 9512

373

153

0 7 11 42

7615

12 17 16 2520 5

41 12

0 0 14615

2595

0 9512

373

153

0 7 11 42

193

12 17 16 2520 5

41 12

0 0 14615

2595

0 0 563

77

0 7 11 42

285

12 17 16 2520 5

41 12

0 0 14615

2595

0 0 563

77

0 0 835

1265

14073

12 17 16 2520 5

41 12

0 0 14615

2595

0 0 0 1287373

0 0 0 0

12 x 1 +17 x 2 +16 x 3 = 25254 x 2 x 3 = 12

14615

x 3 =2595

0 = 1287373



limpiar

Noexistesolucin.


~ ~

~

~

~

~

55 63 41 042 36 42 025 65 31 017 51 12 043 12 44 0

4255

55 63 41 00 666

5558855

0

25 65 31 017 51 12 043 12 44 0

511

55 63 41 00 666

5558855

0

0 40011

13611

0

17 51 12 043 12 44 0

1755

55 63 41 00 666

5558855

0

0 40011

13611

0

0 173455

3755

0

43 12 44 0

4355

55 63 41 00 666

5558855

0

0 40011

13611

0

0 173455

3755

0

0 204955

65755

0

1000333

55 63 41 00 666

5558855

0

0 0 4936111

0

0 173455

3755

0

0 204955

65755

0

289111



~

~

~

(1)

Delaecuacin3delsistema(1)encontramosconlavariablex 3:4936111

x 3=0,x 3=0


x 2=58855

x 3,66655

x 2=58855

0,x 2=0

Delaecuacin1delsistema(1)encontramosconlavariablex 1:55 x 1= 63 x 241 x 3,55 x 1= 630410,x 1=0

Larespuesta:x 1=0,x 2=0,x 3=0

55 63 41 00 666

5558855

0

0 0 4936111

0

0 0 100537

0

0 204955

65755

0

683222

55 63 41 00 666

5558855

0

0 0 4936111

0

0 0 100537

0

0 0 77537

0

30154936

55 63 41 00 666

5558855

0

0 0 4936111

0

0 0 0 00 0 775

370

23254936

55 63 41 00 666

5558855

0

0 0 4936111

0

0 0 0 00 0 0 0

55 x 1 +63 x 2 +41 x 3 = 0

66655

x 2 +58855

x 3 = 0

4936111

x 3 = 0



limpiar

limpiar

Lasolucingeneral:X=

LasolucinporlaregladeCramer:

= =25/576

1= =30897/562= =38287/168

3= =1875/16

x 1=1/=2224584/175x 2=2/=918888/175x 3=3/=2700Larespuesta:x 1=2224584/175x 2=918888/175x 3=2700


~ ~

000

13 x 1

14 x 2 +2 x 3 = 150

38 x 1 +

12 x 2 +

57 x 3 = 213

19 x 1

112

x 2 +12 x 3 = 500

13

14

238

12

57

19

112

12

150 14

2

213 12

57

500 112

12

13

150 238

213 57

19

500 12

13

14

15038

12

21319

112

500

7 5 8 4 64 12 8 6 55 6 5 6 56 4 6 7 8

47

7 5 8 4 60 64

7247

267

117

5 6 5 6 56 4 6 7 8

57



~

~

~

~

(1)


x 4=3613,x 4=

3635


x 3=6932

x 4+1964,13

8 x 3=

6932

+ 1964,x 3=

331280

Delaecuacin2delsistema(1)encontramosconlavariablex 2:647 x 2=

247

x 3267 x 4+

117,647 x 2=

247

267 + 11

7,x 2=

193280

Delaecuacin1delsistema(1)encontramosconlavariablex 1:7 x 1= 5 x 28 x 34 x 4+6,7 x 1=

7 5 8 4 60 64

7247

267

117

0 177

57

227

57

6 4 6 7 8

67

7 5 8 4 60 64

7247

267

117

0 177

57

227

57

0 27

67

257

207

1764

7 5 8 4 60 64

7247

267

117

0 0 138

6932

1964

0 27

67

257

207

132

7 5 8 4 60 64

7247

267

117

0 0 138

6932

1964

0 0 34

5916

9332

613

7 5 8 4 60 64

7247

267

117

0 0 138

6932

1964

0 0 0 3513

3613

7 x 1 +5 x 2 +8 x 3 +4 x 4 = 6647 x 2 +

247 x 3 +

267 x 4 =

117

138 x 3 +

6932

x 4 =1964

3513

x 4 =3613

3635

331280

3635



limpiar

5 8 4 +6,x 1=3356

Larespuesta:x 1=

3356

,

x 2=193280

,

x 3=331280

,

x 4=3635

Lasolucingeneral:X=

Lasolucinporelmtododelamatrizinversa:

AX=B

A=

B=

A1=

Losdetalles

193280

331280

3635

3356

1932803312803635

7 5 8 4 64 12 8 6 55 6 5 6 56 4 6 7 87 4 4 5 105000050000500005000050000

3241963

4481963

10781963

8431963

1651963

851963

1661963

2141963

4151963

1931963

2781963

1731963

7231963

5491963

3311963

2801963

1461963

4741963

3651963

2881963

1641963

2511963

7881963

3541963

2801963



limpiar

limpiar

X=A1*B= =

Anlisisdelacompatibilidaddelsistema.

rango =1rango =1 Losdetalles

Elrangodelamatrizaumentadacoincideconelrangodematrizdecoeficientes,peronocoincideconelnmerodeincgnitas=>elsistemaescompatibleindeterminado .


(1)

Delaecuacin1delsistema(1)encontramosconlavariablex 1:

7 x 1= 5 x 28 x 3+4,x 1=47 57 x 2

87 x 3

Larespuesta:x 1=

87 x 3

57 x 2+

47,

x 2=x 2,

3241963

4481963

10781963

8431963

1651963

851963

1661963

2141963

4151963

1931963

2781963

1731963

7231963

5491963

3311963

2801963

1461963

4741963

3651963

2881963

1641963

2511963

7881963

3541963

2801963

5000050000500005000050000

138000001963

36500001963

27000001963

62500001963

33500001963

7 5 8 47 5 8

7 5 8 4

7 x 1 +5 x 2 +8 x 3 = 4

http://es.wikipedia.org/wiki/Sistema_de_ecuaciones_lineales#Tipos_de_sistemas



limpiar

limpiar

x 3=x 3

Lasolucingeneral:X=


= =25/576

1= =30897/562= =38287/168

3= =1875/16



87 x 3

57 x 2+

47

x 2x 3

13 x 1

14 x 2 +2 x 3 = 150

38 x 1 +

12 x 2 +

57 x 3 = 213

19 x 1

112

x 2 +12 x 3 = 500

13

14

238

12

57

19

112

12

150 14

2

213 12

57

500 112

12

13

150 238

213 57

19

500 12

13

14

15038

12

21319

112

500



= =1963

1= =138000002=

=36500003=

=27000004= =62500005=

=3350000

x 1=1/=13800000/1963x 2=2/=3650000/1963x 3=3/=2700000/1963x 4=4/=6250000/1963x 5=5/=3350000/1963Larespuesta:x 1=13800000/1963x 2=3650000/1963x 3=2700000/1963x 4=6250000/1963x 5=3350000/1963

7 x 1 +5 x 2 +8 x 3 +4 x 4 +6 x 5 = 500004 x 1 +12 x 2 +8 x 3 +6 x 4 +5 x 5 = 500005 x 1 +6 x 2 +5 x 3 +6 x 4 +5 x 5 = 500006 x 1 +4 x 2 +6 x 3 +7 x 4 +8 x 5 = 500007 x 1 +4 x 2 +4 x 3 +5 x 4 +10 x 5 = 50000

7 5 8 4 64 12 8 6 55 6 5 6 56 4 6 7 87 4 4 5 1050000 5 8 4 650000 12 8 6 550000 6 5 6 550000 4 6 7 850000 4 4 5 10

7 50000 8 4 64 50000 8 6 55 50000 5 6 56 50000 6 7 87 50000 4 5 10

7 5 50000 4 64 12 50000 6 55 6 50000 6 56 4 50000 7 87 4 50000 5 10

7 5 8 50000 64 12 8 50000 55 6 5 50000 56 4 6 50000 87 4 4 50000 10

7 5 8 4 500004 12 8 6 500005 6 5 6 500006 4 6 7 500007 4 4 5 50000



limpiar

limpiar


= =25/576

1= =30897/562= =38287/168

3= =1875/16



= =16

1= =322= =803=

13 x 1

14 x 2 +2 x 3 = 150

38 x 1 +

12 x 2 +

57 x 3 = 213

19 x 1

112

x 2 +12 x 3 = 500

13

14

238

12

57

19

112

12

150 14

2

213 12

57

500 112

12

13

150 238

213 57

19

500 12

13

14

15038

12

21319

112

500

x 1 3 x 2 +2 x 3 = 35 x 1 +6 x 2 x 3 = 134 x 1 x 2 +3 x 3 = 8

1 3 25 6 14 1 33 3 213 6 18 1 3

1 3 25 13 14 8 3



limpiar

limpiar

=112

x 1=1/=2x 2=2/=5x 3=3/=7Larespuesta:x 1=2x 2=5x 3=7


= =5

1= =532= =523=

=112

x 1=1/=53/5x 2=2/=52/5x 3=3/=112/5Larespuesta:x 1=53/5x 2=52/5x 3=112/5


= =5

1 3 35 6 134 1 8

x 1 3 x 2 +2 x 3 = 35 x 1 +6 x 2 x 3 = 134 x 1 x 2 +2 x 3 = 8

1 3 25 6 14 1 23 3 213 6 18 1 2

1 3 25 13 14 8 2

1 3 35 6 134 1 8

x 1 3 x 2 +2 x 3 = 35 x 1 +6 x 2 x 3 = 134 x 1 x 2 +2 x 3 = 8

1 3 25 6 14 1 2



limpiar

limpiar

1= =132= =323=

=62



~ ~

~

(1)

Noexistesolucin.


= =5

1= =1432= =1623=

3 3 213 6 18 1 2

1 3 25 13 14 8 2

1 3 35 6 134 1 8

1 3 25 6 14 1 2

5 1 3 20 21 114 1 2

4

1 3 20 21 110 11 6

1121

1 3 20 21 110 0 5

21

x 1 3 x 2 = 221 x 2 = 11

0 = 521

x 1 3 x 2 +2 x 3 = 35 x 1 +6 x 2 x 3 = 134 x 1 x 2 +2 x 3 = 18

1 3 25 6 14 1 23 3 213 6 118 1 2

1 3 25 13 14 18 2



limpiar

limpiar

=322



= =9

1= =1992= =1023=

=266



1 3 35 6 134 1 18

x 1 3 x 2 +2 x 3 = 35 x 1 +6 x 2 + x 3 = 134 x 1 + x 2 +2 x 3 = 18

1 3 25 6 14 1 23 3 213 6 118 1 2

1 3 25 13 14 18 2

1 3 35 6 134 1 18

13 x 1

14 x 2 +2 x 3 = 150

38 x 1 +

12 x 2 +

57 x 3 = 213

19 x 1

12 x 2 +

12 x 3 = 500



mostrarunejemplodeinputdelsistema

2x2y+z=3x+3y2z=13xyz=2

dejeunasceldasvacasparaentrarunasmatricesnocuadradasustedpuedeutilizar:unosfraccinesdecimales(finitosyperidicos): 1/23 , 12.45 , 1.3(56) , 1.2e4 algunasexpresionesaritmticas: 2/3+3*(104) ,(1+x)/y^2 , 2^0.5

utilize Entrar , Barraespaciadora , , , , paranavegarsobrelasclulasarrastreunasmatricesderesultados(arrastrarysoltar )odeuneditordetextoparalateoradematricesyoperacionesconellos,consulte

= =115/448

1= =38337/562= =38287/168

3= =370/3


13

14

238

12

57

19

12

12

150 14

2

213 12

57

500 12

12

13

150 238

213 57

19

500 12

13

14

15038

12

21319

12

500

http://es.wikipedia.org/wiki/Arrastrar_y_soltar



lapginaenlaWikipedia

[email protected] ThankstoPhilipPetrov(http://cphpvb.net)forbulgariantranslation

ThankstoManuelRialCostaforgalegotranslation

http://es.wikipedia.org/wiki/Matriz_(matem%C3%A1ticas)http://cphpvb.net/mailto:[email protected]

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