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Similar matricies

  1. Jun 21, 2007 #1


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    1. The problem statement, all variables and given/known data
    Prove or disprove the following statement:
    If A is a singular matrix (detA=0) the it's similar to a matrix with a row of zeros.

    2. Relevant equations

    3. The attempt at a solution
    I know that A has an e-value 0 which means that it's similar to a matrix that has a column of zeros but how do I relate that to the rows?
  2. jcsd
  3. Jun 21, 2007 #2


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    ok, note that det (M) = product of eigenvalues of M
  4. Jun 21, 2007 #3

    matt grime

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    Since det(A)=0, there is a row relation.

    Or, consider what you do know. A^t has det 0, so there is an M with


    a matrix with a column of zeroes.

    Now how do we get A back out again?
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