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Linear Transformation proof.

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Suppose A is an m x n matrix.

    (a) Let v1 ,...,vn be a basis of ℝn, and Avi = wi ε ℝm, for i = 1,...,n. Prove that the vectors v1,...,vn, w1,...,wn, serve to uniquely specify A.

    (b) Write down a formula for A.


    2. Relevant equations
    Maybe B = T-1 A S



    3. The attempt at a solution

    I said S = { v1,...,vn} and T = {w1,...,wn}, then AS=T..... I kind of get lost from here.

    I think part (b) is suppose to be A = TBS-1.... really not too sure though.
     
    Last edited by a moderator: Apr 17, 2013
  2. jcsd
  3. Apr 17, 2013 #2

    CompuChip

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    So you can write an arbitrary vector as v = a1 v1 + a2 v2 + ... + an vn.
    Does the given information unambiguously define Av now?
    I.e. can you write down the result without reference to A?
     
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