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Homework Help: Linear transformation matrix

  1. Jul 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Let L: R^3 -> R^3 be a linear transformation such that

    L(i) = [1 2 -1], L(j) = [1 0 2] and L(k) = [1 1 3].

    Find L([ 2 -1 3)].

    All the numbers in [ ] should be vertical, but I don't know how to set that up.

    2. Relevant equations



    3. The attempt at a solution

    I'm not sure how to even approach this. I've tried looking at examples in the text and they aren't clear.

    I would think that you make a matrix L with the three columns i j k as above. and x = [2 -1 3] and just calculate Lx=b to find b.

    But a similar problem in the text has a single number answer. I would've guessed that it gives a vector.
     
  2. jcsd
  3. Jul 4, 2010 #2

    radou

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    Homework Helper

    You know how the transformation acts on the basis {i, j, k}. Let v be any vector, then v = αi + βj + γk. Then L(v) = αL(i) + βL(j) + γL(k).

    The vectors L(i), L(j) and L(k) are the columns of the matrix representation of the operator L.
     
  4. Jul 4, 2010 #3

    Office_Shredder

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    Staff Emeritus
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    Gold Member

    You should get a vector here. Maybe you should post the similar problem and we can help you figure out what the difference is?
     
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