Hello I was wondering if anyone could give me confirmation that what I am doing is correct here.
For part a) I have used the fact that addition in linear maps can be split from a singular bracket and made into multiple sums.
So I have wrote out that:
T(x^2 - 2x - 1)= T(x^2) - T(2x) - T(1)
And used the fact that scalars can be brought outside the bracket:
= T(x^2) - 2*T(x) - T(1)
And subbed in the conditions given above the question and got the answer:
= 3x^2 - 5x - 1
Is this correct?