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Linear Algebra and polynomial

  1. Nov 22, 2015 #1
    1. The problem statement, all variables and given/known data

    Let T: P2 --> P3 be the transformation that maps a polynomial p(t) into the polynomial (t+5)p(t).

    a) find the image of p(t)= 2-t+(t^2)
    b) Find the matrix for T relative to bases {1,t,t^2} and {1,t,t^2,t^3}.

    2. Relevant equations
    Given

    3. The attempt at a solution
    a) I know (t+5)p(t)=(t+5)(2-t+(t^2))= 10-3t+4(t^2)+(t^3)

    b) I see in solution T(1) = (t+5) (1)= t+5
    T(t) = (t+5)(t)
    T(t^2)=(t+5)(t^2)
    and so on ...

    My question is why T(1)= 1 and T(t) = t ?! I see that T(1) means p(t)=1 or T(t)=p(t)=t but why is this so ?!
     
  2. jcsd
  3. Nov 22, 2015 #2

    vela

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    T(1) isn't equal to 1, nor is T(t) equal to t. Why do you think they are?
     
  4. Nov 22, 2015 #3
    I see in my solution B={1,t,t^2} and C={1,t,t^2,t^3} Since T(b1)=T(1)=(t+5)(1)=t+5, [T(b1)] relative to C =[5,1,0,0,]
     
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