0 : F - F2 where p(x1, 22, . . . ,27) = (21 + 22, 23 + 27). Prove d is not a linear functional on F7salution To prove that the function up is not linear we need to show a counterexample that violates the properties of linearity consider two vector in mathbbro let's say V = ( 1 , 0 . 1, 0 , 0. 0, 1 ) W = ( 0 . 0, 0 , 0, 0, 0.1 ) How calculate pui cv) and pui ( w). 4 ( v ) = (1to 101 ) = (1,2) 4 ( w ) - ( 050 ) OH1 ) = (0.]) Next let's cheek & i is linear Additivety : 4 ( v two ) = 4 ( 1, 0 , 1 , 0 , 0, 0, 1 ) + (0, 0, 0, 0, 0, 0, 1 = 4 ( 1, 0, 1 0 0 0 2 ) * ( 1, 2 ) spicy ) + prey = ( 1 2 ) + ( 0 1 ) ( 1. 3 )Since 4 ( v two - up ( v ) + 4 (w the adilitivity property isviolated dence W id not a linear danction on math bb p+