problem didn't state, but I assume let V be a vector space: V = C^3 and scalar is C
Define a non-zero linear functional T on C^3 such that T ((1, 1, 1)) = T ((1, 1, −1)) = 0
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!