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## Homework Statement

Let T be the unique linear operator on C

^{3}for which [tex] T_{\epsilon1}=(1,0,i), T_{\epsilon2}=(0,1,1), T_{\epsilon3}=(i,1,0).

[/tex]

Is T invertible?

**2. Homework Equations**

If we show T is non singular or T is onto, then this would imply T is invertible.

## The Attempt at a Solution

I don't really know where to start, I thought about trying to brute force solve the matrix T but I am quite sure there is a more elegant way and hoping someone can give me a kick in that direction.