- #1

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I am having a major brain problem today, with this problem.

L is a linear transform that maps L:P

_{4}[tex]\rightarrow[/tex]P

_{4}

As such that (a

_{1}t

^{3}+a

_{2}t

^{2}+a

_{3}t+a

_{4}= (a

_{1}-a

_{2})t

^{3}+(a

_{3}-a

_{4})t.

I am trying to find the basis for the kernel and range.

I know that the standard basis for P

_{4}is {1,x,x

^{2},x

^{3}}

And the kernel is when L(u)=0, but I don't know how to find the transformation matrix, since we're not dealing with numbers in R, but in the set of polynomials. Is there another way to find the kernel/range and bases without using the T matrix?