Linear transformation and finding the matrix

[fk378]

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?

 

[tiny-tim]

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

Hi fk378!

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) = … ?