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Linear Transformations - Finding the basis for the image

  1. Nov 12, 2007 #1
    1. The problem statement, all variables and given/known data
    Find a basis for the image of the linear transformation T: R^4 -->R^3 given by the formula T(a,b,c,d) = (4a+b -2c - 3d, 2a + b + c - 4d, 6a - 9c + 9d)

    2. Relevant equations

    3. The attempt at a solution

    Well this question followed asking about the basis for the kernel which was easy enough. Unfortunately my notes on this aren't very clear and I don't know where to start.
  2. jcsd
  3. Nov 12, 2007 #2


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    You have 3 equations involving 4 "unknown" parameters. I recommend applying T to (1,0,0,0), (0,1,0,0), (0,0,1,0), and (0,0,0,1) in turn. That will give you 4 vectors in R^3 which clearly cannot be independent. A basis will be a subset of that set of 4 vectors. What space do they span?
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