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Math Help - Linear Transformation and Matrices

  1. #1
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    Linear Transformation and Matrices

    Let L: P1 --> P2 be define be L(p(t)) = tp(t) + p(0). Consider the ordered bases S={t,1} and S'={t+1, t-1} for P1 and T={t2, t, 1} and T'={t2+1, t-1, t+1} for P2. Find the representation of L with respect to:
    a) S and T
    b) S' and T'
    c) Find L(-3t-3) by using the definition of : and the matrices obtained in parts (a) and (b).
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  2. #2
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    I honestly have no idea where to start with this. I understand the simple examples that they provide in the books, but I am not sure how to do this...
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  3. #3
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    first, define the images under L of the basis vectors of S, and express these as linear combinations of the basis T. from this, the matrix for L w.r.t. these bases should be clear. then do the same for S' and T'.

    i'll get you started:

    L(1) = t = (0)t^2 + (1)t + (1)1
    L(t) = t^2 = (1)t^2 + (0)t + (0)1.

    in other words L(p(t)) = L((a1,a2)S) = L(a1(t) + a2(1)) = a1(L(t)) + a2(L(1)) = a1(t^2 + 0t + 0) + a2(0t^2 + t + 1) = (a1t^2 + a2t + a2) = (a1,a2,a2)T

    part (a) will be the easy part, because S and T are the normal bases you expect for P1 and P2.

    part (b) will be trickier because the S'-coordinates for at + b are not (a,b), and the T'-coordinates for ct^2 + dt + e are not (c,d,e).

    look at THIS thread: http://www.mathhelpforum.com/math-he...es-177570.html
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