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Linear Mappings & Proofs

  1. Sep 19, 2009 #1
    1. Hi!
    I was wondering if anyone could help me to solve the following problem!
    Let L : [R][n] ->[R][m] and M :[R][m]-> [R][m] be linear mappings.
    Prove that if M is invertible, then rank (M o L) = rank (L)


    thanks!! :)
     
  2. jcsd
  3. Sep 19, 2009 #2

    HallsofIvy

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    If M is invertible it maps Rm one-to-one onto Rm. In particular, it maps any k dimensional subset of Rm onto a k dimensional subset of Rm. Now, what does "rank" mean?
     
  4. Sep 19, 2009 #3
    the dimension of the column space of M is the rank of M

    and we know that dim (null M)= 0 since the null space of M is just the zero vector
    and since rank = m - (dimension of the null space of M)
    so rank is m?
     
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