1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Transformations (polynomials/matrices)

  1. Nov 17, 2007 #1
    [SOLVED] Linear Transformations (polynomials/matrices)

    Never mind, I can see it now, thanks

    1. The problem statement, all variables and given/known data
    Let S be the linear transformation on P2 into P3 over R. S(p(x)) = xp(x)
    Let T be the linear transformation on P3 over R into R2x2 defined by T(a0 + a1x + a2x^2 + a3x^3) = [ a0 a1; a2 a3]

    Find a formula for TS(p(x)).

    3. The attempt at a solution
    The first thing I do is find the S(A) where A is the standard basis of P2 and I place that into a transition matrix from the basis B (std. basis of P3).
    B,A = [0,0,0;1,0,0;0,1,0;0,0,1]
    Then I do the similar steps for fining [T]C,B where C = E2x2
    [T]C,B = I4 (identity matrix of a 4x4)
    Multiplying the matrix yields: [T]* = [0,0,0;1,0,0;0,1,0;0,0,1]

    I am fairly positive that the math up to this point is accurate. (I get the correct range of T).

    My question is how do I specifically find the formula for TS(p(x)) using the last matrix that I found? I know it's a mapping of P2 into R2x2, but I don't quite see how they get [0, a0; a1, a2] as the matrix. I know it lines up with TS, but still
     
    Last edited: Nov 17, 2007
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Linear Transformations (polynomials/matrices)
Loading...