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Math Help - linear functions

  1. #1
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    linear functions

    which of the following functions is not linear?
    a)for all x€R, f(x)=(x; 2x)
    b) for all (x; y; z)€R3, f(x; y; z)=x-2y+3z
    c) for all (x; y) € R2, f(x; y)= (x+1; y-1)
    d) they're all linear

    And why???

    I hope it's clear enough to understand...These things are driving me crazy, any help is really appreciated..thanks
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  2. #2
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    Quote Originally Posted by 0123 View Post
    which of the following functions is not linear?
    a)for all x€R, f(x)=(x; 2x)
    b) for all (x; y; z)€R3, f(x; y; z)=x-2y+3z
    c) for all (x; y) € R2, f(x; y)= (x+1; y-1)
    d) they're all linear

    And why???

    I hope it's clear enough to understand...These things are driving me crazy, any help is really appreciated..thanks
    A linear function of a single variable is,
    f(x)=ax+b
    And several variables is,
    f(x_1,x_2,...,x_n)=a_1x_1+a_2x_2+...+a_nx_n+b
    It is just a combination of all exponents to the first power of all the variables.
    Thus, the answer is the 4th choice.
    Last edited by ThePerfectHacker; December 27th 2006 at 10:22 AM.
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  3. #3
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    I can't see the reasoning behind the answer(latex doesn't work) but I can tell you that the right answer is c, that is the third. But I can't see why. Any idea?thanks
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  4. #4
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    If by ‘linear’ you mean ‘linear transformation’ then the function in part (c) is not linear: note that f(0,0)=(1,1).
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  5. #5
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    I am not much into this math part but the solution provided by the book is c. We talked of this linear functions after the matrix argument and said that f is linear when there exist a matrix such that y=Ax( and talked about homogeneity and additivity....... ) help please
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  6. #6
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    Note that f(0,0)=(1,1). To be a linear transformation we need f(0,0)=(0,0).
    In each of these we can see the mappings as a linear transformation from one linear space to another. One property of linear transformations is that they map the ‘zero point’ to the ‘zero point’. That is a necessary but not sufficient property for a linear transformation.
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