You have to express (1,0,0), and the other two basis vectors, as linear combinations of (1,0,1), (2,1,2) and (0,1,1). If for example you know that (1,0,0) = –(1,0,1) + (2,1,2) – (0,1,1) then (since T is a linear transformation) T(1,0,0) = –T(1,0,1) + T(2,1,2) – T(0,1,1) = –v+v–v = –v.

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