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Math Help - find matrices that ..

  1. #1
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    find matrices that ..

    hi everyone. im having some trouble with this question...








    thank you!



    EDIT: I think I found the answer ... for part a) would it be

    0 0 1
    0 1 0
    1 0 0

    (so an identity matrix flipped horizontally?)
    Last edited by finalfantasy; February 19th 2009 at 02:48 PM.
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  2. #2
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    Quote Originally Posted by finalfantasy View Post
    EDIT: I think I found the answer ... for part a) would it be
    0 0 1
    0 1 0
    1 0 0
    Not according to my CAS. Look again at the third power it is back to the original.
    But try <br />
\left( {\begin{array}{ccc}<br />
   0 & 0 & 1  \\<br />
   1 & 0 & 0  \\<br />
   0 & 0 & 0  \\ \end{array} } \right)
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  3. #3
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    Thanks!


    would i use the property of determinants to solve part b? (this assignment is about determinants)
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  4. #4
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    Quote Originally Posted by finalfantasy View Post
    this assignment is about determinants
    As such can you use \left| {AB} \right| = \left| A \right|\left| B \right| to prove that \left| {A^k } \right| = \left| A \right|^k ?
    If you can, then that answers your question.
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  5. #5
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    hm .. what i ended up doing was stating that if B inverse exists, then det (B) cannot equal zero.

    i used the example from part one to illustrate that, and the det. was zero therefore there was no inverse. can that suffice as answer?
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