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Very simple linear algebra question:

  1. Mar 2, 2008 #1
    This is a very basic question, but I am not understanding the concept here.

    it asks, consider the linear transformation:

    y_1(y subscript 1) = x_2 - x_3
    y_2 = x_1*x_3
    y_3 = x_1 - x_2

    Can anyone explain why this is not linear? I am not sure what the criteria is and the book doesn't have any example like this reasoned out.

    Thank you.
  2. jcsd
  3. Mar 2, 2008 #2
    A transformation T is linear if T(cv) = cT(v) and T(v+w) = T(v) + T(w) for all scalars c and vectors v and w. Does this help?
  4. Mar 2, 2008 #3


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    In particular, look at what happens to y2.
  5. Mar 2, 2008 #4
    Ok, so for y_2:

    x(x_1*x_3) is not the same as...?

    I am not sure how to apply this. Can someone explain how to proceed?
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