In each case, show that U is T-invariant, use it to find a block upper triangular matrix for T, and use that to compute c1(x).
(a) T: P2 → P2, T{a + bx + cx2) = (-a + 2b + c) + (a + 3b + c)x + {a + 4b)x2, U = span{l, x + .v}
(b) T : P2 → P2, T{a + bx + cx2) = (5a - 2b + c)
+ (5a - b + c)x + {a + 2c)x2,
U = span(l - 2x2, x + x-2)