Question

let T:P1->P2 be defined by T(p(x))=xP(x)
Find the bases for Im(T) and Ker(T)

Answer 1

@TuringTest help pls

Answer 2

i'm not sure i did this!
natural basis for P1 is {1,x^2}
T(1)=x
T(x)=x^2

Im(T)=<x,x^2>

let a,b b element of R
a=0 , b=0
T:P1->P2, T[P(x)]=x[P(x)]
thus Im(T)=<X,X^2>

Answer 3

@REMAINDER

Answer 4

you are correct
then
dim(im(T)+dim(ker(T))=dim(P1)
2+dim(ker(T))=2
thus dim(ker(T))=0
then ker{0v}

Answer 5

thanks a bunch neh, o tlalefile