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Math Help - Invertible formulas problem

  1. #1
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    Invertible formulas problem

    Determine which of the formulas hold for all invertible matrices and

    A. is invertible
    B.
    C.
    D.
    E.
    F. is invertible

    I have to select which of the above are true. I thought I was right in picking A, C and F. However, I was apparently wrong.

    Any help is greatly appreciated. Thanks in advance!
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  2. #2
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    Quote Originally Posted by elven06 View Post
    Determine which of the formulas hold for all invertible matrices and

    A. is invertible
    B.
    C.
    D.
    E.
    F. is invertible

    I have to select which of the above are true. I thought I was right in picking A, C and F. However, I was apparently wrong.

    Any help is greatly appreciated. Thanks in advance!

    A and E are the only true ones. Now try to show, by counterexamples, why.

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    A and E are the only true ones. Now try to show, by counterexamples, why.

    Tonio
    Is this some sort of rule? You seemed to figure it out really fast. I have another problem of a similar nature, I don't really know how to go about tackling it:

    Which of the following sets are subspaces of ?

    A.
    B. arbitrary number
    C. arbitrary number
    D. arbitrary number
    E.
    F.
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  4. #4
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    For the first question a lot of them can be solved by remembering some Matrix multiplication rules. ABC = (AB)C = A(BC). However AB does not equal BA.

    For the second question remember the requirements for a subspace: Does the space contain the zero vector? If V and U are in the subspace then is V+U is also in the subspace? for some scalar r if U is in the subspace is rU in the subspace? If you answered yes to all of the previous questions then it is a subspace. If you answered no to any one of them it is not.
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