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Vector spaces, closed under addition

  1. Mar 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Let
    S={A (element) M2(R) : det(A) = 0}

    (b) Give an explicit example illustrating that S is not closed under matrix addition.


    2. Relevant equations



    3. The attempt at a solution

    1) I think that the problem is saying S is a set of 2x2 matrices, whose determinant is zero?

    2) I'm also not exactly sure what it means by "explicit example". What I put down was this:

    5rbb7.jpg

    Is this the right way of approaching it? det(a) is zero, det(b) is zero, so they are members of S. But, adding a and b together gives a new matrix that doesn't have a determinant of zero.
     
  2. jcsd
  3. Mar 8, 2009 #2

    Dick

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    Science Advisor
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    I think that's exactly what they were asking for.
     
  4. Mar 8, 2009 #3
    Pulled through once again, Dick. Thanks for the clarification! :smile:
     
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