Question

Prove that t is a linear transformation given that t(1,-1,1)=(1,0) and t(1,1,1)=(0,1)

Answer 1

Let T:R2→R3T:R2→R3 be the linear transformation such that T(1,1)=(1,0,2)T(1,1)=(1,0,2) and T(2,3)=(1,−1,4)T(2,3)=(1,−1,4). 

Does such a linear transformation exist?

So far I've worked out that it cannot exist, as the first entry for T(1,1)T(1,1) is 1, 
whereas the first entry for T(2,3)T(2,3) is 1, which can only be obtained through 3-2, or half of 2.

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