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Homework Help: Linear algebra change of coordinates

  1. Mar 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Consider a transformation T in the vector space consisting of linear transformation T: V -> V with a basis B = {b1, ..., bn} for V. Show that {k1, ..., kv} is a basis for Ker(T) if and only if {[k1]B, ..., [kv)B} is a basis for Nul([T]B) and that {r1, ..., rq} is a basis for Range(T) if and only if {[r1]B, ..., [rq]} is a basis for Col([T]B).

    The notation [ ]B indicates that it is a coordinate vector.


    2. Relevant equations
    Not sure that there are any.


    3. The attempt at a solution
    I just don't get how to relate everything... I don't know how to think about it all which means I don't really have any good attempts.
     
  2. jcsd
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