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chm

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## Homework Statement

problem didn't state, but I assume let V be a vector space: V = C^3 and scalar is C

## Homework Equations

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!