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Math Help - Linear Transformation

  1. #1
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    Linear Transformation

    Hi There,

    Just need some help with this question, would really appreciate your help,

    Let u1 = (1,2,1), u2 = (0,1,1) and u3=(1,1,1)
    Also let v1 = (1,2,3,4) v2 = (1,0,1,0) and v3 = (2,1,0,3)

    Find a Matrix A such that Ta(uk)= vk for all 1<=k<=3

    Have an exam coming up and I'm stumped on this
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  2. #2
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    Quote Originally Posted by Ben85 View Post
    Hi There,

    Just need some help with this question, would really appreciate your help,

    Let u1 = (1,2,1), u2 = (0,1,1) and u3=(1,1,1)
    Also let v1 = (1,2,3,4) v2 = (1,0,1,0) and v3 = (2,1,0,3)

    Find a Matrix A such that Ta(uk)= vk for all 1<=k<=3

    Have an exam coming up and I'm stumped on this
    The first thing you need to do is find a way of expressing this transformation. Express v1 given u1, v2 given u2 and v3 given u3. From there you can construct the matrix that you want, which will satisfy T(u)=Au=v.

    Matrix A times the column vector [u1,u2,u3] will equal [v1,v2,v3,v4] (imagine those are columns). So A must be a 4x3 matrix and will be multiplied by the 3x1 column matrix for u, resulting in a 4x1 column matrix representing v. Each row in A will [a1,a2,a3] such that a1u1+a2u2+a3u3=v1.
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