1. The problem statement, all variables and given/known data 3. The attempt at a solution So, first I wrote, [itex]T(X) = λ_1 X, T(Y) = λ_2 Y[/itex] If [itex]λ_1 = λ_2[/itex]: [itex]T(X+Y) = T(X) + T(Y) = λ_1 X + λ_2 Y = λ_1 (X+Y)[/itex], so this does indeed seem to be an eigenvector. But I'm less convinced for the case [itex]λ_1 ≠ λ_2[/itex]. Again, I get the transformation down to the form: [itex]λ_1 X + λ_2 Y[/itex] But if eigenvalues are necessarily one constant, then I don't see how I pull constants out as above. How do I go about showing this?