Exploring Linear Transformations on Basis Elements of P3(R)

[Butelle]

Hi

I am trying to do a math assignment and I am finding it really difficult.

Assume you have a linear transformation from T: P3(R) --> R4

What relevance is there to applying the transformation to the basis elements of P3(R), ie: T(1), T(x), T(x^2), T(x^3)? Why is this subset special? How does it help determine the range of T?

Thanks.

 

[latentcorpse]

dim(P^3)=dim(\mahtbb{R}^4)=4

you have the basis elements of P^3.

The action of T on each of these basis elements will let you know the basis elements of \mathbb{R}^4

i.e. 1,x,x^2,x^3 are the basis elements of P^3
and T(1),T(x),T(X^2),T(x^3) are the basis elemetns of \mathbb{R}^4

applying T to any element of p(x) \in P^3 will yield T(p(x)) \in \mathbb{R}^4 and T(p(x))=aT(1)+bT(x)+cT(x^2)+dT(x^3) where a,b,c,d \in \mathbb{Z}

 

[Butelle]

thank you!