Final answer:
Without additional information on the linear transformation T, such as the image of another basis vector, it is impossible to determine T([0, 1]).
Step-by-step explanation:
The linear transformation T from ℝ² to ℝ³ is given by the transformation of a basis vector [1, 0] to [1, -4, 4]. However, to find T([0, 1]), we need additional information which is not provided in the question. Since linear transformations are completely determined by their effect on a basis of the domain, without knowing T([0, 1]), or any other basis vector transformation except T([1, 0]), we cannot deduce T([0, 1]).