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I Question On Linear Independence

  1. Nov 2, 2016 #1
    We were going over linear independents in class and my professor said that if y1 and y2 are linearly independent then the ratio of y2/y1 is not a constant, but he never explained why it is not a constant.
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  3. Nov 2, 2016 #2


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    You can turn it around: if y1 and y2 are linearly dependent, there is a ##\lambda## such that ##y_1 = \lambda y_2##
  4. Nov 2, 2016 #3


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    Given that you posted this in a differential equations subforum, I take it that ##y_1## and ##y_2## belong to some vector space of functions that contains the solutions of a certain linear differential equation?

    Provided this is indeed your setting, what (by definition) does it mean when ##y_{1,2}## are independent? What does it mean when they are dependent?
  5. Nov 2, 2016 #4


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    Minor point -- you were going over linear independence in class. Linear independence is an attribute of a set of vectors of other elements that belong to a vector space.
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