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Math Help - Help in proving (cA)^p = c^p*A^p for any matrix A

  1. #1
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    Help in proving (cA)^p = c^p*A^p for any matrix A

    Hello,

    I am stuck on the following problem:

    If p is a nonnegative integer and c is a scalar, show that
    (cA)^p = c^p A^p

    Here is what I have started:

    \textrm{Let } A=[a_{ij}] \textrm{ be any } n \times n matrix. Then

     (cA)^p=([ca_{ij}])^p

    Where could I go from here? Is this a good first start?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Fourier View Post
    Hello,

    I am stuck on the following problem:

    If p is a nonnegative integer and c is a scalar, show that
    (cA)^p = c^p A^p

    Here is what I have started:

    \textrm{Let } A=[a_{ij}] \textrm{ be any } n \times n matrix. Then

     (cA)^p=([ca_{ij}])^p

    Where could I go from here? Is this a good first start?
    Almost there!
     (cA)^p=([ca_{ij}])^p  = c^p [a_{ij} ]^p = c^pA^p

    -Dan
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