Tarea Regla de cramer

Unidad 3. Determinantes

Actividad 2. Regla de Cramer

Resuelve el siguiente sistema de ecuaciones utilizando la regla de Cramer.

a)

x+2y+3z= 4

-4x+3y+5z= 2

 3x+3y - 4z= -2

Ax = b

A= [pic 2]

x = [pic 3]

b = [pic 4]

A=  x =  b = [pic 5][pic 6][pic 7]

A1 =  A2=   A3= [pic 8][pic 9][pic 10]

D1 = |A1| = 4 (-12 -15) -2 (-8 +10) + 3 (6 + 6) = -108 – 4 + 36 =  -76

D2 = |A2| = 1 (-8 + 10) -4 (16 - 15) + 3 (8 - 6) = 2 – 4 + 6 =  4

D3 = |A3| = 1 (-6 -6) -2 (8 -6) + 4 (-12 - 9) = -12 – 4 - 84 =  -100

D = |A|

D = 1 (-12-15) -2 (16 – 15) + 3 (-12 – 9) = -27 -2 -63 = -92

X1 = -76/-92 = 19/23

X2 = 4/-92 =-1/23

X3 = -100/-92

b)

x+2y+5z= 1

3x-4y+2z= 4

 2x+4y + 10z=2

Ax = b

A= [pic 11]

x = [pic 12]

b = [pic 13]

A=  x =  b = [pic 14][pic 15][pic 16]

A1 =  A2=   A3= [pic 17][pic 18][pic 19]

D1 = |A1| = 1 (-40 -8) -2 (40 - 4) + 5 (16 + 8) = -48 – 72 + 120 =  0

D2 = |A2| = 1 (40 - 4) -1 (30 - 4) + 5 (6 - 8) = 36 – 26 - 10 =  0

D3 = |A3| = 1 (-8 -16) -2 (6 -8) + 1 (12 + 8) = -24 + 4 + 20 =  0

D = |A|

D = 1 (-40-8) -2 (30 – 4) + 5 (12 + 8) = -48 -52 + 100 = 0

X1 = 0

X2 = 0

X3 = 0

c)

3x-2y=1

5x-6y= 2

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