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Sum of invertible matrices is invertible?

  1. Oct 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Is the sum of two invertible matrices necessarily invertible?


    3. The attempt at a solution

    I don't know plz help.
     
  2. jcsd
  3. Oct 5, 2008 #2

    statdad

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    Homework Helper

    Re: Matrices

    Try a couple of small examples - use [tex] 2 \times 2 [/tex]
    matrices that you know are invertible.

    One small hint: both [tex] 2 [/tex] and [tex] -2 [/tex] are invertible real numbers, but their sum isn't invertible.
     
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