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Linear transformation with standard basis

  1. Mar 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Let s be the linear transformation
    s: P2→ R^3 ( P2 is polynomial of degree 2 or less)
    a+bx→(a,b,a+b)
    find the matrix of s and the matrix of tos with respect to the standard basis for the domain
    P2 and the standard basis for the codomain R^3



    3. The attempt at a solution
    Now I know that Standard basis of P2 is {1,x}
    and standard basis for R^3 = {(1,0,0), (0,1,0), (0,0,1)}
    and s(1)= (1,0,1)
    and s(x) = (0,1,1)

    but I don't know how to proceed from here?
     
  2. jcsd
  3. Mar 19, 2012 #2
    Well we know s: P2 -> R3 so the map of s will have 2 columns and 3 rows. The first row will be (1, 0). Can you do the rest?

    To find the matrix with respect to P2's basis and R3's basis, you proceed by taking a vector in P2, applying s to it, then expressing the result using R3's basis. Repeating this for each vector in P2 gives the matrix. How do these compare?

    You might find this helpful: http://www.millersville.edu/~bikenaga/linear-algebra/matrix-linear-trans/matrix-linear-trans.html [Broken].

    It might be helpful to think of the resultant matrix as a way of "translating" between the languages of P2 and R3.

    Hope that helps!
     
    Last edited by a moderator: May 5, 2017
  4. Mar 19, 2012 #3
    Thanks. I'll try and post back my findings.
     
  5. Mar 20, 2012 #4
    am I correct?
     
    Last edited: Mar 20, 2012
  6. Mar 20, 2012 #5
    still working on it
     
    Last edited: Mar 20, 2012
  7. Mar 20, 2012 #6
    trying not suceeded
     
  8. Mar 20, 2012 #7
    i resolved it no help needed
     
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