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Homework Help: Linear Algebra Help

  1. Feb 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Give a proof:
    Let C be a square matrix.
    Show if C^(k+1)=0,
    then I-C is nonsingular and (I-C)^-1=I+C+C^2+...+C^k.


    2. Relevant equations
    I don't know.
    I can't find a theorm that will help me.


    3. The attempt at a solution
    I know if a matrix is nonsingular, it has an inverse.
     
  2. jcsd
  3. Feb 8, 2010 #2
    You need no theorem, one can see it directly, because , (I-C)(I+C+...+C^k)=I-C^(k+1)=I which means, that I-C is invertable, and the inverse is the above.
     
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