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Conditions for linear independence

  1. Dec 14, 2011 #1
    1. The problem statement, all variables and given/known data
    Under what conditions on the numbers a and b are the vectors (1,a), (1,b) linearly independent in R2?


    2. Relevant equations



    3. The attempt at a solution
    x(1,a)+y(1,b)=(0,0)
    (x,ax)+(y,by)=(0,0)
    (x+y, ax+by)=(0,0)
    x+y=0, ax+by=0
    x=-y, ax=-by
    unsure where to go from here...
     
  2. jcsd
  3. Dec 14, 2011 #2

    Deveno

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    Science Advisor

    what does it mean for two vectors to be linearly independent?

    (hint: the answer is NOT:

    there exist c1,c2 such that c1v1+c2v2 = 0).
     
  4. Dec 15, 2011 #3

    HallsofIvy

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    Staff Emeritus
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    Good hint!!
     
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