Is there a linear transformation T : R3 -> R2 such that T(1, -1, 1) = (1, 0) and T(1, 1, 1) = (0, 1)? Justify your answer.
I tried using the definition of a linear map to make a contradiction so to prove there is not a linear transformation that meets the above requirements. But I don't think I proved anything that way. For all I know, there could be a linear transformation that meets the above requirements but I don't know how to find it.