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Let $T: P_2 \to R^2$ be linear given by $T(a + bx + cx^2) = (a-b, b+c) $ . Find the matrix of T with respect to the base $\{1, x, x^2\}$ (of $P_2$) and $\{(1, 0), (-2, 1)\}$

This is the problem in my textbook. It looks so strange with me, I don't know how to use information $(1,0), (-2,1)$ to solve this problem.

Thanks :)

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1 Answer 1

$T(1)=(1,0), T(x)=(-1,1), T(x^2)=(0,1)$. Now write the right-hand-sizes as a unique linear combination of $(1,0), (-2,1)$. It will build up the matrix of $T$.

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