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Linear transformation and finding the matrix

  • Thread starter fk378
  • Start date
  • #1
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Homework Statement


Define T: P2-->R3 by
T(p)=
[p(-1)]
[p(0)]
[p(1)]

Find the matrix for T relative to the basis {1,t,t^2} for P2 and the standard basis for R3.


The Attempt at a Solution



I'm not sure how to go about this. Start off by computing T(1)? But am I trying to see what the transformation does to p(t)=1 or just 1?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Find the matrix for T relative to the basis {1,t,t^2} for P2 and the standard basis for R3.
Hi fk378! :smile:

I'm assuming that P2 is the quadratic expressions with real coefficients.

So the vector (a,b,c) in P2 relative to the basis {1,t,t^2} is at² + bt + c.

Then (a,b,c)(-1) = … ? (a,b,c)(0) = … ? (a,b,c)(1) = … ? :smile:
 

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