Let V be the subspace of C[0, 2] spanned by the vectors 1, sin x, and cos x, and let T : V R3 be the evaluation transformation at the sequence of points 0, , 2. Find (a) T(1 + sin x + cos x) (b) ker(T ) (c) R(T )

a c 4 116 '&tl a cEcL*)= Ko e @ + C-r'\s,,/tttTs9l' -r'@s*lt+CPslflar9' e UtnltlicnP;r)*/v=...