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Homework Help: Answer check and explanation(Linear transformation)

  1. Mar 28, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the standard matrix of the following linear transformation:

    T(x1, x2, x3, x4) = (-2 x1 - 5 x2 - 4 x3 - x4, 2 x1 + 2 x2 - 5 x3 + x4)

    3. The attempt at a solution

    [x1,x2,x3,x4] [-2,2;-5,2;-4,-5;-1,1]
    =[-2 x1 - 5 x2 - 4 x3 - x4, 2 x1 + 2 x2 - 5 x3 + x4]

    T(e1) = (-2,2)
    T(e2) = (-5,2)
    T(e3) = (-4,-5)
    T(e4) = (-1,1)

    A = [-2,-5,-4,-1; 2,2,-5,1]

    The answer has been checked to be correct. But I'm not seeing why the standard matrix has to be transposed?
  2. jcsd
  3. Mar 28, 2014 #2


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    Science Advisor
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    Gold Member

    A matrix representing a transformation from ##R^4 \to R^2## would be a 2x4 matrix. The images of the basis vectors give the columns. Nothing is transposed that I see.
    Last edited: Mar 28, 2014
  4. Mar 28, 2014 #3


    Staff: Mentor

    There are two problems with the above:
    1. You have your x vector on the wrong side of A (it should be Ax rather than xA), and your matrix is wrong. You have four rows with two columns - it should be two rows with four columns.
    The vectors on the right are all column vectors.
    The transformation is T: R4 → R2, so the matrix for T will by 2 X 4 (i.e., two rows with four columns each).
  5. Mar 29, 2014 #4
    Both of you guys are correct.
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