first of all, it should be [UT] = [U]*[T], yes?

secondly, please attempt to write your problem out in your question. attached images of photos are very hard to read, and a lot of posters here won't even bother opening attachments. there is an entire forum section devoted to LaTex and how to use it, you should at the very least give the tutorial thread a look-see.

without going into the extraordinate amount of detail required to check all your work, i can only indicate that i suspect your matrices are wrong, because your computation of T is wrong.

if T(f(x)) = f'(x)(3+x) + 2f(x), then T(1-x) = (-1)(3+x) + 2(1-x) = -3 - 3x + 2 - 2x = -5x - 1, not -1 - 3x as you have.