4. Define T : P, - P, by T p = p0 - pit + p 2 t2. a. Show that Tis a linear transformation. b. Find T(p) when p(t) = -2 + t. Is p an eigenvector of T? " Find the matrix for T relative to the basis { 1, t, t for P2.4) Define T: 12- the by TG = plo) - plant + plz)t? ( ) Show that T is a hner transformation. b ] T (p ) = T ( - 2 +t ) 4 ) Find T(p) when plot ) = - 2 it. Is pon eigenvedor of T ? = ( - 2 ) - ( - 2 + 1 ) t + ( 2- 2) +2 ( ) Find the matrix for T relative to the basis flit, t' ] for Piz. = - 2+t ( ) T lets ) = ( pts ) ( 1 - ( pts) (At + ( pig ) ( 2 ) + 2 = 1 . ( . 2 +( ) = T (p ) = ( plo ) - p ( i) t + pl zz t ? ) + ( gles - quilt + 9(2) ( ? ) . . it is on eigenvector = Tup ) + T (g ) T cup ) = (cp) (o) - Cop ) cn t + ( cp ] (2) tz C ) TLD = 1 - 1+ + 1. t 2 = ( ( Plo ) - PCIt + P(2 ) ( 2 ) T ( t ) = 0 . 1. 1 + 2. f2 = ( TCP ) :. liver fromformation T(t' ) = 0 - 1.1 + 412