My question is about Transition matrices, I want to ask the following question:
Given a Linear transformation $T:R^2\to R^2,$ Such that:
$$T(x, y) = (3x-y, x-2y).$$
Let $B$ be basis for $R^2$ such that:
$$B=\bigl((1, 1), (2, 5) \bigr) $$
- Use transition matrices to calculate $[T]^B_B$ by $[T]^E_E$ .
I tried to calculate it by the following formula:
$$[T]^B_B=[I]^E_B[T]^E_E[I]^B_E$$
and i got wrong result, I know other ways to calculate it, but i have no choice and it must to be done by transition matrices and $[T]^E_E$ , any suggestions?