Algo

1.-

3X₁ + 6X₂ + 6X₃ = 9 3 6 6 9 R₁(1/3)

2X₁ - 5X₂ + 4X₃ = 6 2 -5 4 6

5X₁ +28 X₂ -26X₃= -8 5 28 -26 -8

1 2 2 3 1 2 2 3

2 -5 4 6 A₁₂(-2) 0 -9 0 6 R₂(1/9)

5 28 -26 -8 A₂₃(-5) 0 18 -36 -23

1 2 2 3 1 2 2 3

0 1 0 0 0 1 0 0

0 18 -36 -23 A₂₃(-18) 0 0 -36 -23 R₃(-1/36)

1 2 2 3 X₁ + 2X₂ + 2X₃ =30 1 0 0 X₂ =0

0 0 1 23/36 X₃= 23/36

X₁ + 2X₂ + 2X₃ = 3
X₁ + 2(0)+2(23/36) =3
X₁ + 23/18=3
X₁=3-23/18=31/18

COMPROBACION
3X₁ + 6X₂ + 6X₃ = 9 2X₁ - 5X₂ + 4X₃ = 6
3(31/18) + 6(0) + 6(23/36) = 9 2(31/18) - 5(0) + 4(23/36) = 6
31/6 + 35/6=9 31/9 + 23/9 = 6
9=9 6 = 6

5X₁ +28X₂ -26X₃= -8
5(31/18) + 28( 0) -26(23/36)=-8
155/18 – 299/18 =-8
-8=-8
2.-

X₁ - 2X₂ + X₃ + X₄ = 2 1 -2 1 1 2 A₁₂(-3)

3X₁ +2X₃ - 2X₄ = -8 3 0 2 -2 -8

4X₂ - X₃ - X₄ =1 0 4 -1 -1 1

5X₁ + 3X₃ - X₄ = -3 5 0 3 -1 -3 A₁₄(-5)

1 -2 1 1 2 1 -2 1 1 2

0 6 -1 -5 -14 R₂(1/6) 0 1 -1/6 -5/6 -7/3

0 4 -1 -1 1 0 4 -1 -1 1 A₂₃(-4)

0 10 -2 -6 -130 10 -2 -6 -13 A₂₄(-10)

1 -2 1 1 2 1 -2 1 1 2

0 1 -1/6 -5/6 -7/3 0 1 -1/6 -5/6 -7/3

0 0 -5/3 7/3 31/3 R₃(-3/5) 0 0 1 -7/5 -31/5

0 0 -1/3 7/3 31/3 0 0 -1/3 7/3 31/3

1 -2 1 1 2

A₃₄(1/3) 0 1 -1/6 -5/6 -7/3

0 0 1 -7/5 -31/5

0 0 0 28/15 124/15 R₄(15/28)

1 -2 1 1 2 X₁ -2X₂ + X₃ + X₄=2

0 1 -1/6 -5/6 -7/3 X₂- 1/6X₃ - 5/6X₄= -7/3

0 0 1 -7/5-31/5 X₃ - 7/5X₄ = -31/5

0 0 0 1 31/7 X₄= 31/7

X₃ - 7/5X₄ = -31/5 X₂- 1/6X₃ - 5/6X₄= -7/3 X₁ -2X₂ + X₃ + X₄=2

X₃ - 7/5(31/7) = -31/5 X₂- 1/6(0) - 5/6(31/7)= -7/3 X₁ -2(19/14) + 0 + 31/7=2

X₃ - 31/5 = -31/5 X₂- 155/42= -7/3 X₁ - 19/7 + 31/7 = 2

X₃ = -31/5 + 31/5 X₂=-7/3 + 155/42 X₁ + 12/7 =2

X₃ =0X₂=-19/14 X₁ =2/7

COMPROBACION:

X₁ - 2X₂ + X₃ + X₄ = 2 3X₁ +2X₃ - 2X₄ = -8

2/7-2(19/14)+0+31/7=2 3(2/7) +2(0) – 2(31/7) = -8

2/7-19/7+31/7=2 6/7-62/7=-8

14/7=2 -8=-8

2=2

4X₂ - X₃ - X₄ =1

4(19/14)-0-31/7=1

76/14 – 31/7=11=1

3.-

X₁ + 2X₂ - X₃ + X₄ = 7

3X₁ + 6X₂ -3 X₃ +3 X₄ = 21

1 2 -1 1 7 1 2 -1 1 7

3 6 -3 3 21 A₁₂(-3) 0 0 0 0 -19

EL SISTEMA NO TIENE SOLUCION

4.-

X₁ + X₂= 4 1 1 4 1 1 4

2X₁ - 3X₂ =7 2 -3 7 A₁₂(-2) 0 -5 -1 R₂(-1/5)

3X₁-2X₂ =11 3 -2 11| A₁₃(-3) 0 -5 -1

1 1 4 X₁+X₂=4 X₁+ 1/5=4

0 1 1/5 X₂=1/5 X₁=4-1/5

0 0 0 X₃=V.A X₁=19/5

COMPROBACION:

X₁+ X₂= 4 2X₁ - 3X₂ =7 3X₁-2X₂ =11

19/5 + 1/5= 4 2(19/5)-3(1/5)=7 3(19/5)-2(1/5)=11

20/5=4 38/5-3/5=7 57/5-2/5=11

4=4 35/5=7 55/5=11

7=7 11=11

5.-

X₁ - 2X₂ + X₃ + X₄ = 2

3X₁ +2X₃ - 2X₄ = -8

4X₂ - X₃ - X₄ =1

-X₁ + 6X₂ - 2X₃ = 7

1 -2 1 1 2 A₁₂(-3)

3 0 2 -2 -8

0 4 -1 -1 1

-1 6 -2 0 7 A₁₄(-1)

1 -2 1 1 2 1 -2 1 1 2

0 6 -1 -5 -14R₂(1/6) 0 1 -1/6 -5/6 -7/3

0 4 -1 -1 1 0 4 -1 -1 1 A₂₃(-4)

0 8 -3 -1 5 0 8 -3 -1 5 A₂₄(-8)

1 -2 1 1 2 1 -2 1 1 2

0 1 -1/6 -5/6 -7/3 0 1 -1/6 -5/6 -7/3

0 0 -5/3 7/3 31/3 R₃(-3/5) 0 0 1 -7/5 -31/5

0 0 -5/3 17/3/3 71/3 0 0 -5/3 17/3 71/3

1 -2 1 1 2

A₃₄(5/3) 0 1 -1/6 -5/6 -7/3

0 0 1 -7/5 -31/5

0 0 0 10/3 40/3 R₄(3/10)

1 -2 1 1 20 1 -1/6 -5/6 -7/3

0 0 1 -7/5 -31/5

0 0 0 1 4

X₁ - 2X₂ + X₃ + X₄ = 2 X₂ - 1/6X₃ - 5/6X₄ = -7/3

X₂ - 1/6X₃ - 5/6X₄ = -7/3 X₂ - 1/6(-3/5) - 5/6(4) = -7/3

X₃ - 7/5X₄ =-31/5 X₂ + 1/10- 10/3=-7/3

X₄ = 4 X₂ = -7/3 + 97/30

X₃ - 7/5X₄ =-31/5 X₂ =9/10

X₃ - 7/5(4) =-31/5 X₁ - 2X₂ + X₃ + X₄ = 2

X₃ - 28/5 =-31/5 X₁ -...