Metodos para resolver sistemas de Ecuaciones Lineales(Exactos)41009143-6 HENRY FRANCISCO MARTINEZ1) Resolver el siguiente sistema por el mtodo de Gauss

-65341

448321.5

54725

-69654

Inicia La Triangulacion Inferior:

i = 0 _________________________________________________________________________

j = 1

Auxiliar = M[1][0]/M[0][0] = 4.000/-6.000 = -0.667

k = 0

M[1][0] = M[1][0] - M[0][0] * Aux = 4.000 - -6.000 * -0.667 = 0.000

M[1][0] = 0.000

k = 1

M[1][1] = M[1][1] - M[0][1] * Aux = 4.000 - 5.000 * -0.667 = 7.333

M[1][1] = 7.333

k = 2

M[1][2] = M[1][2] - M[0][2] * Aux = 8.000 - 3.000 * -0.667 = 10.000

M[1][2] = 10.000

k = 3

M[1][3] = M[1][3] - M[0][3] * Aux = 3.000 - 4.000 * -0.667 = 5.667

M[1][3] = 5.667

k = 4

M[1][4] = M[1][4] - M[0][4] * Aux = 2.000 - 1.000 * -0.667 = 2.667

M[1][4] = 2.667

i = 0 _________________________________________________________________________

j = 2

Auxiliar = M[2][0]/M[0][0] = 5.000/-6.000 = -0.833

k = 0

M[2][0] = M[2][0] - M[0][0] * Aux = 5.000 - -6.000 * -0.833 = -0.000

M[2][0] = -0.000

k = 1

M[2][1] = M[2][1] - M[0][1] * Aux = 4.000 - 5.000 * -0.833 = 8.167

M[2][1] = 8.167

k = 2

M[2][2] = M[2][2] - M[0][2] * Aux = 7.000 - 3.000 * -0.833 = 9.500

M[2][2] = 9.500

k = 3

M[2][3] = M[2][3] - M[0][3] * Aux = 2.000 - 4.000 * -0.833 = 5.333

M[2][3] = 5.333

k = 4

M[2][4] = M[2][4] - M[0][4] * Aux = 5.000 - 1.000 * -0.833 = 5.833

M[2][4] = 5.833

i = 0 _________________________________________________________________________

j = 3

Auxiliar = M[3][0]/M[0][0] = -6.000/-6.000 = 1.000

k = 0

M[3][0] = M[3][0] - M[0][0] * Aux = -6.000 - -6.000 * 1.000 = 0.000

M[3][0] = 0.000

k = 1

M[3][1] = M[3][1] - M[0][1] * Aux = 9.000 - 5.000 * 1.000 = 4.000

M[3][1] = 4.000

k = 2

M[3][2] = M[3][2] - M[0][2] * Aux = 6.000 - 3.000 * 1.000 = 3.000

M[3][2] = 3.000

k = 3

M[3][3] = M[3][3] - M[0][3] * Aux = 5.000 - 4.000 * 1.000 = 1.000

M[3][3] = 1.000

k = 4

M[3][4] = M[3][4] - M[0][4] * Aux = 4.000 - 1.000 * 1.000 = 3.000

M[3][4] = 3.000

Su Matriz :

-6.000 5.000 3.000 4.000 1.000

0.000 7.333 10.000 5.667 2.667

-0.000 8.167 9.500 5.333 5.833

0.000 4.000 3.000 1.000 3.000

i = 1 _________________________________________________________________________

j = 2

Auxiliar = M[2][1]/M[1][1] = 8.167/7.333 = 1.114

k = 1

M[2][1] = M[2][1] - M[1][1] * Aux = 8.167 - 7.333 * 1.114 = 0.000

M[2][1] = 0.000

k = 2

M[2][2] = M[2][2] - M[1][2] * Aux = 9.500 - 10.000 * 1.114 = -1.636

M[2][2] = -1.636

k = 3

M[2][3] = M[2][3] - M[1][3] * Aux = 5.333 - 5.667 * 1.114 = -0.977

M[2][3] = -0.977

k = 4

M[2][4] = M[2][4] - M[1][4] * Aux = 5.833 - 2.667 * 1.114 = 2.864

M[2][4] = 2.864

i = 1 _________________________________________________________________________

j = 3

Auxiliar = M[3][1]/M[1][1] = 4.000/7.333 = 0.545

k = 1

M[3][1] = M[3][1] - M[1][1] * Aux = 4.000 - 7.333 * 0.545 = -0.000

M[3][1] = -0.000

k = 2

M[3][2] = M[3][2] - M[1][2] * Aux = 3.000 - 10.000 * 0.545 = -2.455

M[3][2] = -2.455

k = 3

M[3][3] = M[3][3] - M[1][3] * Aux = 1.000 - 5.667 * 0.545 = -2.091

M[3][3] = -2.091

k = 4

M[3][4] = M[3][4] - M[1][4] * Aux = 3.000 - 2.667 * 0.545 = 1.545

M[3][4] = 1.545

Su Matriz :

-6.000 5.000 3.000 4.000 1.000

0.000 7.333 10.000 5.667 2.667

-0.000 0.000 -1.636 -0.977 2.864

0.000 -0.000 -2.455 -2.091 1.545

i = 2 _________________________________________________________________________

j = 3

Auxiliar = M[3][2]/M[2][2] = -2.455/-1.636 = 1.500

k = 2

M[3][2] = M[3][2] - M[2][2] * Aux = -2.455 - -1.636 * 1.500 = 0.000

M[3][2] = 0.000

k = 3

M[3][3] = M[3][3] - M[2][3] * Aux = -2.091 - -0.977 * 1.500 = -0.625

M[3][3] = -0.625

k = 4

M[3][4] = M[3][4] - M[2][4] * Aux = 1.545 - 2.864 * 1.500 = -2.750

M[3][4] = -2.750

Su Matriz :

-6.000 5.000 3.000 4.000 1.000

0.000 7.333 10.000 5.667 2.667

-0.000 0.000 -1.636 -0.977 2.864

0.000 -0.000 0.000 -0.625 -2.750

Inicia la Sustitucion hacia atras

X[3] = Matriz[3][4]/Matriz[3][3] = 4.400

Suma = ( M[2][3] * X[3] )

Suma = ( -4.300 )= -4.300

X[2] = (Matriz[2][4] - Suma) / Matriz[2][2] =( 2.864 - -4.300 ) / -1.636

X[2] = -4.378

Suma = ( M[1][2] * X[2] + M[1][3] * X[3] )

Suma = ( -43.778 + 24.933 )= -18.844

X[1] = (Matriz[1][4] - Suma) / Matriz[1][1] =( 2.667 - -18.844 ) / 7.333

X[1] = 2.933

Suma = ( M[0][1] * X[1] + M[0][2] * X[2] + M[0][3] * X[3] )

Suma = ( 14.667 + -13.133 + 17.600 )= 19.133

X[0] = (Matriz[0][4] - Suma) / Matriz[0][0] =( 1.000 - 19.133 ) / -6.000

X[0] = 3.022

Su vector Solucion es :

X[0] --> 3.0222222222222190

X[1] --> 2.9333333333333300

X[2] --> -4.3777777777777729

X[3] --> 4.3999999999999959

2) Resolver el siguiente sistema por el mtodo de Gauss-Jordan

545-6

34531

2457

DetA= 0 No tiene nica solucin

3) Resolver el siguiente sistema por el mtodo de Inversin de Matrices

-63145

144341

37253

48-682

Inicia La Triangulacion Inferior:

i = 0 _________________________________________________________________________

j = 1

Auxiliar = M[1][0]/M[0][0] = 1.000/-6.000 = -0.167

k = 0

M[1][0] = M[1][0] - M[0][0] * Aux = 1.000 - -6.000 * -0.167 = 0.000

M[1][0] = 0.000

k = 1

M[1][1] = M[1][1] - M[0][1] * Aux = 4.000 - 3.000 * -0.167 = 4.500

M[1][1] = 4.500

k = 2

M[1][2] = M[1][2] - M[0][2] * Aux = 4.000 - 1.000 * -0.167 = 4.167

M[1][2] = 4.167

k = 3

M[1][3] = M[1][3] - M[0][3] * Aux = 3.000 - 4.000 * -0.167 = 3.667

M[1][3] = 3.667

k = 4

M[1][4] = M[1][4] - M[0][4] * Aux = 0.000 - 1.000 * -0.167 = 0.167

M[1][4] = 0.167

k = 5

M[1][5] = M[1][5] - M[0][5] * Aux = 1.000 - 0.000 * -0.167 = 1.000

M[1][5] = 1.000

k = 6

M[1][6] = M[1][6] - M[0][6] * Aux = 0.000 - 0.000 * -0.167 = 0.000

M[1][6] = 0.000

k = 7

M[1][7] = M[1][7] - M[0][7] * Aux = 0.000 - 0.000 * -0.167 = 0.000

M[1][7] = 0.000

i = 0 _________________________________________________________________________

j = 2

Auxiliar = M[2][0]/M[0][0] = 3.000/-6.000 = -0.500

k = 0

M[2][0] = M[2][0] - M[0][0] * Aux = 3.000 - -6.000 * -0.500 = 0.000

M[2][0] = 0.000

k = 1

M[2][1] = M[2][1] - M[0][1] * Aux = 7.000 - 3.000 * -0.500 = 8.500

M[2][1] = 8.500

k = 2

M[2][2] = M[2][2] - M[0][2] * Aux = 2.000 - 1.000 * -0.500 = 2.500

M[2][2] = 2.500

k = 3

M[2][3] = M[2][3] - M[0][3] * Aux = 5.000 - 4.000 * -0.500 = 7.000

M[2][3] = 7.000

k = 4

M[2][4] = M[2][4] - M[0][4] * Aux = 0.000 - 1.000 * -0.500 = 0.500

M[2][4] = 0.500

k = 5

M[2][5] = M[2][5] - M[0][5] * Aux = 0.000 - 0.000 * -0.500 = 0.000

M[2][5] = 0.000

k = 6

M[2][6] = M[2][6] - M[0][6] * Aux = 1.000 - 0.000 * -0.500 = 1.000

M[2][6] = 1.000

k = 7

M[2][7] = M[2][7] - M[0][7] * Aux = 0.000 - 0.000 * -0.500 = 0.000

M[2][7] = 0.000

i = 0 _________________________________________________________________________

j = 3

Auxiliar = M[3][0]/M[0][0] = 4.000/-6.000 = -0.667

k = 0

M[3][0] = M[3][0] - M[0][0] * Aux = 4.000 - -6.000 * -0.667 = 0.000

M[3][0] = 0.000

k = 1

M[3][1] = M[3][1] - M[0][1] * Aux = 8.000 - 3.000 * -0.667 = 10.000

M[3][1] = 10.000

k = 2

M[3][2] = M[3][2] - M[0][2] * Aux = -6.000 - 1.000 * -0.667 = -5.333

M[3][2] = -5.333

k = 3

M[3][3] = M[3][3] - M[0][3] * Aux = 8.000 - 4.000 * -0.667 = 10.667

M[3][3] = 10.667

k = 4

M[3][4] = M[3][4] - M[0][4] * Aux = 0.000 - 1.000 * -0.667 = 0.667

M[3][4] = 0.667

k = 5

M[3][5] = M[3][5] - M[0][5] * Aux = 0.000 - 0.000 * -0.667 = 0.000

M[3][5] = 0.000

k = 6

M[3][6] = M[3][6] - M[0][6] * Aux = 0.000 - 0.000 * -0.667 = 0.000

M[3][6] = 0.000

k = 7

M[3][7] = M[3][7] - M[0][7] * Aux = 1.000 - 0.000 * -0.667 = 1.000

M[3][7] = 1.000

Su Matriz :

-6.000 3.000 1.000 4.000 1.000 0.000 0.000 0.000

0.000 4.500 4.167 3.667 0.167 1.000 0.000 0.000

0.000 8.500 2.500 7.000 0.500 0.000 1.000 0.000

0.000 10.000 -5.333 10.667 0.667 0.000 0.000 1.000

i = 1 _________________________________________________________________________

j = 2

Auxiliar = M[2][1]/M[1][1] = 8.500/4.500 = 1.889

k = 1

M[2][1] = M[2][1] - M[1][1] * Aux = 8.500 - 4.500 * 1.889 = 0.000

M[2][1] = 0.000

k = 2

M[2][2] = M[2][2] - M[1][2] * Aux = 2.500 - 4.167 * 1.889 = -5.370

M[2][2] = -5.370

k = 3

M[2][3] = M[2][3] - M[1][3] * Aux = 7.000 - 3.667 * 1.889 = 0.074

M[2][3] = 0.074

k = 4

M[2][4] = M[2][4] - M[1][4] * Aux = 0.500 - 0.167 * 1.889 = 0.185

M[2][4] = 0.185

k = 5

M[2][5] = M[2][5] - M[1][5] * Aux = 0.000 - 1.000 * 1.889 = -1.889

M[2][5] = -1.889

k = 6

M[2][6] = M[2][6] - M[1][6] * Aux = 1.000 - 0.000 * 1.889 = 1.000

M[2][6] = 1.000

k = 7

M[2][7] = M[2][7] - M[1][7] * Aux = 0.000 - 0.000 * 1.889 = 0.000

M[2][7] = 0.000

i = 1 _________________________________________________________________________

j = 3

Auxiliar = M[3][1]/M[1][1] = 10.000/4.500 = 2.222

k = 1

M[3][1] = M[3][1] - M[1][1] * Aux = 10.000 - 4.500 * 2.222 = -0.000

M[3][1] = -0.000

k = 2

M[3][2] = M[3][2] - M[1][2] * Aux = -5.333 - 4.167 * 2.222 = -14.593

M[3][2] = -14.593

k = 3

M[3][3] = M[3][3] - M[1][3] * Aux = 10.667 - 3.667 * 2.222 = 2.519

M[3][3] = 2.519

k = 4

M[3][4] = M[3][4] - M[1][4] * Aux = 0.667 - 0.167 * 2.222 = 0.296

M[3][4] = 0.296

k = 5

M[3][5] = M[3][5] - M[1][5] * Aux = 0.000 - 1.000 * 2.222 = -2.222

M[3][5] = -2.222

k = 6

M[3][6] = M[3][6] - M[1][6] * Aux = 0.000 - 0.000 * 2.222 = 0.000

M[3][6] = 0.000

k = 7

M[3][7] = M[3][7] - M[1][7] * Aux = 1.000 - 0.000 * 2.222 = 1.000

M[3][7] = 1.000

Su Matriz :

-6.000 3.000 1.000 4.000 1.000 0.000 0.000 0.000

0.000 4.500 4.167 3.667 0.167 1.000 0.000 0.000

0.000 0.000 -5.370 0.074 0.185 -1.889 1.000 0.000

0.000 -0.000 -14.593 2.519 0.296 -2.222 0.000 1.000

i = 2 _________________________________________________________________________

j = 3

Auxiliar = M[3][2]/M[2][2] = -14.593/-5.370 = 2.717

k = 2

M[3][2] = M[3][2] - M[2][2] * Aux = -14.593 - -5.370 * 2.717 = -0.000

M[3][2] = -0.000

k = 3

M[3][3] = M[3][3] - M[2][3] * Aux = 2.519 - 0.074 * 2.717 = 2.317

M[3][3] = 2.317

k = 4

M[3][4] = M[3][4] - M[2][4] * Aux = 0.296 - 0.185 * 2.717 = -0.207

M[3][4] = -0.207

k = 5

M[3][5] = M[3][5] - M[2][5] * Aux = -2.222 - -1.889 * 2.717 = 2.910

M[3][5] = 2.910

k = 6

M[3][6] = M[3][6] - M[2][6] * Aux = 0.000 - 1.000 * 2.717 = -2.717

M[3][6] = -2.717

k = 7

M[3][7] = M[3][7] - M[2][7] * Aux = 1.000 - 0.000 * 2.717 = 1.000

M[3][7] = 1.000

Su Matriz :

-6.000 3.000 1.000 4.000 1.000 0.000 0.000 0.000

0.000 4.500 4.167 3.667 0.167 1.000 0.000 0.000

0.000 0.000 -5.370 0.074 0.185 -1.889 1.000 0.000

0.000 -0.000 -0.000 2.317 -0.207 2.910 -2.717 1.000

4) Resolver el siguiente sistema por el mtodo de Inversin de Matrices particionadas

411145

423251

1531012.5

24-6233

325314

Auxiliar = M[1][0]/M[0][0] = 4.000/4.000 = 1.000

k = 0

M[1][0] = M[1][0] - M[0][0] * Aux = 4.000 - 4.000 * 1.000 = 0.000

M[1][0] = 0.000

k = 1

M[1][1] = M[1][1] - M[0][1] * Aux = 2.000 - 1.000 * 1.000 = 1.000

M[1][1] = 1.000

k = 2

M[1][2] = M[1][2] - M[0][2] * Aux = 3.000 - 1.000 * 1.000 = 2.000

M[1][2] = 2.000

k = 3

M[1][3] = M[1][3] - M[0][3] * Aux = 2.000 - 1.000 * 1.000 = 1.000

M[1][3] = 1.000

k = 4

M[1][4] = M[1][4] - M[0][4] * Aux = 5.000 - 4.000 * 1.000 = 1.000

M[1][4] = 1.000

k = 5

M[1][5] = M[1][5] - M[0][5] * Aux = 1.000 - 5.000 * 1.000 = -4.000

M[1][5] = -4.000

i = 0 _________________________________________________________________________

j = 2

Auxiliar = M[2][0]/M[0][0] = 1.000/4.000 = 0.250

k = 0

M[2][0] = M[2][0] - M[0][0] * Aux = 1.000 - 4.000 * 0.250 = 0.000

M[2][0] = 0.000

k = 1

M[2][1] = M[2][1] - M[0][1] * Aux = 5.000 - 1.000 * 0.250 = 4.750

M[2][1] = 4.750

k = 2

M[2][2] = M[2][2] - M[0][2] * Aux = 3.000 - 1.000 * 0.250 = 2.750

M[2][2] = 2.750

k = 3

M[2][3] = M[2][3] - M[0][3] * Aux = 1.000 - 1.000 * 0.250 = 0.750

M[2][3] = 0.750

k = 4

M[2][4] = M[2][4] - M[0][4] * Aux = 0.000 - 4.000 * 0.250 = -1.000

M[2][4] = -1.000

k = 5

M[2][5] = M[2][5] - M[0][5] * Aux = 1.000 - 5.000 * 0.250 = -0.250

M[2][5] = -0.250

i = 0 _________________________________________________________________________

j = 3

Auxiliar = M[3][0]/M[0][0] = 2.000/4.000 = 0.500

k = 0

M[3][0] = M[3][0] - M[0][0] * Aux = 2.000 - 4.000 * 0.500 = 0.000

M[3][0] = 0.000

k = 1

M[3][1] = M[3][1] - M[0][1] * Aux = 4.000 - 1.000 * 0.500 = 3.500

M[3][1] = 3.500

k = 2

M[3][2] = M[3][2] - M[0][2] * Aux = -6.000 - 1.000 * 0.500 = -6.500

M[3][2] = -6.500

k = 3

M[3][3] = M[3][3] - M[0][3] * Aux = 2.000 - 1.000 * 0.500 = 1.500

M[3][3] = 1.500

k = 4

M[3][4] = M[3][4] - M[0][4] * Aux = 3.000 - 4.000 * 0.500 = 1.000

M[3][4] = 1.000

k = 5

M[3][5] = M[3][5] - M[0][5] * Aux = 3.000 - 5.000 * 0.500 = 0.500

M[3][5] = 0.500

i = 0 _________________________________________________________________________

j = 4

Auxiliar = M[4][0]/M[0][0] = 3.000/4.000 = 0.750

k = 0

M[4][0] = M[4][0] - M[0][0] * Aux = 3.000 - 4.000 * 0.750 = 0.000

M[4][0] = 0.000

k = 1

M[4][1] = M[4][1] - M[0][1] * Aux = 2.000 - 1.000 * 0.750 = 1.250

M[4][1] = 1.250

k = 2

M[4][2] = M[4][2] - M[0][2] * Aux = 5.000 - 1.000 * 0.750 = 4.250

M[4][2] = 4.250

k = 3

M[4][3] = M[4][3] - M[0][3] * Aux = 3.000 - 1.000 * 0.750 = 2.250

M[4][3] = 2.250

k = 4

M[4][4] = M[4][4] - M[0][4] * Aux = 1.000 - 4.000 * 0.750 = -2.000

M[4][4] = -2.000

k = 5

M[4][5] = M[4][5] - M[0][5] * Aux = 4.000 - 5.000 * 0.750 = 0.250

M[4][5] = 0.250

Su Matriz :

4.000 1.000 1.000 1.000 4.000 5.000

0.000 1.000 2.000 1.000 1.000 -4.000

0.000 4.750 2.750 0.750 -1.000 -0.250

0.000 3.500 -6.500 1.500 1.000 0.500

0.000 1.250 4.250 2.250 -2.000 0.250

i = 1 _________________________________________________________________________

j = 2

Auxiliar = M[2][1]/M[1][1] = 4.750/1.000 = 4.750

k = 1

M[2][1] = M[2][1] - M[1][1] * Aux = 4.750 - 1.000 * 4.750 = 0.000

M[2][1] = 0.000

k = 2

M[2][2] = M[2][2] - M[1][2] * Aux = 2.750 - 2.000 * 4.750 = -6.750

M[2][2] = -6.750

k = 3

M[2][3] = M[2][3] - M[1][3] * Aux = 0.750 - 1.000 * 4.750 = -4.000

M[2][3] = -4.000

k = 4

M[2][4] = M[2][4] - M[1][4] * Aux = -1.000 - 1.000 * 4.750 = -5.750

M[2][4] = -5.750

k = 5

M[2][5] = M[2][5] - M[1][5] * Aux = -0.250 - -4.000 * 4.750 = 18.750

M[2][5] = 18.750

i = 1 _________________________________________________________________________

j = 3

Auxiliar = M[3][1]/M[1][1] = 3.500/1.000 = 3.500

k = 1

M[3][1] = M[3][1] - M[1][1] * Aux = 3.500 - 1.000 * 3.500 = 0.000

M[3][1] = 0.000

k = 2

M[3][2] = M[3][2] - M[1][2] * Aux = -6.500 - 2.000 * 3.500 = -13.500

M[3][2] = -13.500

k = 3

M[3][3] = M[3][3] - M[1][3] * Aux = 1.500 - 1.000 * 3.500 = -2.000

M[3][3] = -2.000

k = 4

M[3][4] = M[3][4] - M[1][4] * Aux = 1.000 - 1.000 * 3.500 = -2.500

M[3][4] = -2.500

k = 5

M[3][5] = M[3][5] - M[1][5] * Aux = 0.500 - -4.000 * 3.500 = 14.500

M[3][5] = 14.500

i = 1 _________________________________________________________________________

j = 4

Auxiliar = M[4][1]/M[1][1] = 1.250/1.000 = 1.250

k = 1

M[4][1] = M[4][1] - M[1][1] * Aux = 1.250 - 1.000 * 1.250 = 0.000

M[4][1] = 0.000

k = 2

M[4][2] = M[4][2] - M[1][2] * Aux = 4.250 - 2.000 * 1.250 = 1.750

M[4][2] = 1.750

k = 3

M[4][3] = M[4][3] - M[1][3] * Aux = 2.250 - 1.000 * 1.250 = 1.000

M[4][3] = 1.000

k = 4

M[4][4] = M[4][4] - M[1][4] * Aux = -2.000 - 1.000 * 1.250 = -3.250

M[4][4] = -3.250

k = 5

M[4][5] = M[4][5] - M[1][5] * Aux = 0.250 - -4.000 * 1.250 = 5.250

M[4][5] = 5.250

Su Matriz :

4.000 1.000 1.000 1.000 4.000 5.000

0.000 1.000 2.000 1.000 1.000 -4.000

0.000 0.000 -6.750 -4.000 -5.750 18.750

0.000 0.000 -13.500 -2.000 -2.500 14.500

0.000 0.000 1.750 1.000 -3.250 5.250

i = 2 _________________________________________________________________________

j = 3

Auxiliar = M[3][2]/M[2][2] = -13.500/-6.750 = 2.000

k = 2

M[3][2] = M[3][2] - M[2][2] * Aux = -13.500 - -6.750 * 2.000 = 0.000

M[3][2] = 0.000

k = 3

M[3][3] = M[3][3] - M[2][3] * Aux = -2.000 - -4.000 * 2.000 = 6.000

M[3][3] = 6.000

k = 4

M[3][4] = M[3][4] - M[2][4] * Aux = -2.500 - -5.750 * 2.000 = 9.000

M[3][4] = 9.000

k = 5

M[3][5] = M[3][5] - M[2][5] * Aux = 14.500 - 18.750 * 2.000 = -23.000

M[3][5] = -23.000

i = 2 _________________________________________________________________________

j = 4

Auxiliar = M[4][2]/M[2][2] = 1.750/-6.750 = -0.259

k = 2

M[4][2] = M[4][2] - M[2][2] * Aux = 1.750 - -6.750 * -0.259 = 0.000

M[4][2] = 0.000

k = 3

M[4][3] = M[4][3] - M[2][3] * Aux = 1.000 - -4.000 * -0.259 = -0.037

M[4][3] = -0.037

k = 4

M[4][4] = M[4][4] - M[2][4] * Aux = -3.250 - -5.750 * -0.259 = -4.741

M[4][4] = -4.741

k = 5

M[4][5] = M[4][5] - M[2][5] * Aux = 5.250 - 18.750 * -0.259 = 10.111

M[4][5] = 10.111

Su Matriz :

4.000 1.000 1.000 1.000 4.000 5.000

0.000 1.000 2.000 1.000 1.000 -4.000

0.000 0.000 -6.750 -4.000 -5.750 18.750

0.000 0.000 0.000 6.000 9.000 -23.000

0.000 0.000 0.000 -0.037 -4.741 10.111

i = 3 _________________________________________________________________________

j = 4

Auxiliar = M[4][3]/M[3][3] = -0.037/6.000 = -0.006

k = 3

M[4][3] = M[4][3] - M[3][3] * Aux = -0.037 - 6.000 * -0.006 = -0.000

M[4][3] = -0.000

k = 4

M[4][4] = M[4][4] - M[3][4] * Aux = -4.741 - 9.000 * -0.006 = -4.685

M[4][4] = -4.685

k = 5

M[4][5] = M[4][5] - M[3][5] * Aux = 10.111 - -23.000 * -0.006 = 9.969

M[4][5] = 9.969

Su Matriz :

4.000 1.000 1.000 1.000 4.000 5.000

0.000 1.000 2.000 1.000 1.000 -4.000

0.000 0.000 -6.750 -4.000 -5.750 18.750

0.000 0.000 0.000 6.000 9.000 -23.000

0.000 0.000 0.000 -0.000 -4.685 9.969

5) Resolver el siguiente sistema por el mtodo de Jauss-Jordan particionado

511231

4-63143

5335252

54-6788

152348

6) Resolver el siguiente sistema por el mtodo de Intercambio

14244

4578-62

43455

12124

x1x2x3x4

b11 4 2 4

b24 5 7 8

b34 3 4 5

b41 2 1 2

x1x2x3b2

b1-1 1 1/2 -1 1/2 1/2

x2- 1/2 - 5/8 - 7/8 1/8

b31 1/2 - 1/8 - 3/8 5/8

b40 3/4 - 3/4 1/4

x1 x2b1b2

X3- 2/3 1 - 2/3 1/3

x2 1/12 -1 1/2 7/12 - 1/6

b31 3/4 - 1/2 1/4 1/2

b4 1/2 0 1/2 0

b3x2b1b2

x3- 8/21 17/21 - 4/7 - 1/3

x2 1/21 -1 10/21 4/7 - 1/12

x1 4/7 2/7 - 1/7 1

b4 2/7 1/7 3/7 1/2

b1b2b3b4

x1-1 0 0 2 4 x119 2/3

x2-3 -3 1/2 -2 7 -6 x2-36 5/6

x3-3 -3 1/6 -2 5 2/3 5 x34

x45 5 1/12 3 -10 1/3 4 x427