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For example: $T: P_2 \to P_5$ given by $T(p(x)) = x^3(p(x))$

How would I find the kernel and range for this?

All I know is that $\dim(\ker T)+ \dim(\operatorname{image}T)= \dim(p_2)$.

Therefore, $\dim(\ker T)+ \dim(\operatorname{image}T)=3$?

Also, how do I represent T by a matrix with respect to bases for the domain and codomain?

Any help at all is appreciated, as I really have absolutely no idea what I am doing.

Thanks in advance!

1 Answers 1