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Matrix determinants.

  1. May 23, 2013 #1
    1. The problem statement, all variables and given/known data
    For which values of x is the matrix (see attachment) invertible?

    2. Relevant equations
    Row ops. Cofactors etc..

    3. The attempt at a solution
    Well, a matrix is only invertible when it's determinant is non zero. I've begun doing some row ops and have just hit a little snag. If you look at the attachment you'll see that I can facto (1 - x) out from the minor matrix. I remember hearing in a lecture that you have to factor out (1 - x) from both the top and bottom row of the matrix (i.e. you'll have (1 -x)^2 factored out instead of just (1 - x). Could somebody explain why you don't just factor out (1 - x) one like you would with factoring a scalar out of a matrix as normal?x
  2. jcsd
  3. May 23, 2013 #2
  4. May 23, 2013 #3


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    Homework Helper

    In the reduced 2x2 matrix, the factor (1-x) is common to all of the members of the matrix. You can only factor it out once. Whatever you heard about factoring the matrix was incorrect.

    See this article: http://en.wikipedia.org/wiki/Matrix_(mathematics)

    specific topic: scalar multiplication ofa matrix
  5. May 23, 2013 #4
    Thanks for clearing that up.
  6. May 23, 2013 #5


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    Even with a scalar, wikipedia confirms that to scale a row by m scales the determinant by m, which is clear if you think of the formula for the determinant.
  7. May 23, 2013 #6
    Yeah. That's actually what got me thinking about it in the first place.
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