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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?

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# Basis for kernel of linear transform

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