Let S = {(1, 2, -1), (1, 1, -1), (2, 1, 1)} and B = {u, v, w} be bases for $R^3$. Suppose that the
$\begin{bmatrix} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$
transition matrix from B to S is P =
Which one in the below is B?
A. {(2, 0, -2), (1, 1, -1), (3, 4, 5)}
B. {(1, 0, 1), (1, 1, -1), (3, 3, 0)}
C. {(1, 1, 1), (1, 1, 3), (3, 3, 1)}
D. {(1, 0, 1), (2, 1, 3), (3, 0, 1)}
E. {(2, 3, -2), (1, 1, -1), (3, 3, 0)}