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algebra lineal (kolmanejer32sec1.6)

Module by: daniel chavez. E-mail the author

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ejercicio algebralineal,kolman.. 32 seccion 1.6

Sea

f x y z = 1 2 3 - 3 - 2 - 1 - 2 0 2 f x y z = 1 2 3 - 3 - 2 - 1 - 2 0 2 (1)

determine x,y,zx,y,z tales que

f x y z = 2 2 4 f x y z = 2 2 4 (2)

Plan

  • Escribimos la matriz extendida
  • Hacemos reducción de Gauss Jordan
  • Interpretamos los resultados para determinar x,y,zx,y,z

Ejecución

redsage] blue A = matrix([[1,2,3,2],[-3,-2,-1,2],[-2,0,2,4]])

redsage] blueA

1232-3-2-12-20241232-3-2-12-2024

redsage] blueA.echelon_form()

123204880000123204880000

Esto quiere decir que:

z ∈ R 4 y + 8 z = 8 x + 2 y + 3 z = 2 z ∈ R 4 y + 8 z = 8 x + 2 y + 3 z = 2 (3)

redsage] bluex,y,z = var('x, y,z')

redsage] blue solve([x + 2*y + 3*z ==2, 4*y + 8*z == 8], x, y, z)

x=r1-2,y=2-2r1,z=r1x=r1-2,y=2-2r1,z=r1

Esto en su forma vectorial es igual a

x y z = - 2 2 0 + 1 - 2 1 r , r ∈ R x y z = - 2 2 0 + 1 - 2 1 r , r ∈ R (4)

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