1. The problem statement, all variables and given/known data problem didn't state, but I assume let V be a vector space: V = C^3 and scalar is C 2. Relevant equations Define a non-zero linear functional T on C^3 such that T ((1, 1, 1)) = T ((1, 1, −1)) = 0 3. The attempt at a solution So let X1 = (1, 1, 1); X2 = (1, 1, -1); It asks me to define a non zero linear functional, that means I need to define T(x) = α1T(x1) + α2T(X2) ? Since T(X1) = T(X2) = 0 then T(X) = 0 then it's not the answer. I'm stuck here. Can anyone give me a hint please? Thanks!