- #1

TranscendArcu

- 285

- 0

## Homework Statement

## 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?