Extending the basis of a T-invariant subspace

Let ##T: V → V ## be a linear map on a finite-dimensional vector space ##V##.
Let ##W## be a T-invariant subspace of ##V##.
Let ##γ## be a basis for ##W##.

Then we can extend ##γ## to ##γ \cup S##, a basis for ##V##, where ##γ \cap S = ∅ ##, so that ## W \bigoplus span(S) = V ##.

My question:
Is ##span(S)## a T-invariant subspace of ##V##?

I've been trying to prove it is, but am not sure. I would like some assistance, so I know where I might steer my proof. Thanks!

EDIT: Never mind just solved it. It's false!

BiP

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