Question
Let $T$ be a linear transformation from $P_{2}$ into $P_{2}$ such that $T(1)=x, T(x)=1+x,$ and $T\left(x^{2}\right)=1+x+x^{2}$. Find $T\left(2-6 x+x^{2}\right)$.
Step 1
We have: \[T\left(2-6 x+x^{2}\right) = 2T(1) - 6T(x) + T\left(x^{2}\right)\] Show more…
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