# Let $A = \begin{bmatrix} 0 & 9 \\ -1 & 6 \end{bmatrix}$ and $B=\{b_1,b_2\}$, where

Let $$A = \begin{bmatrix} 0 & 9 \\ -1 & 6 \end{bmatrix}$$ and $$B=\{b_1,b_2\}$$, where $$b_1=\begin{bmatrix} 3 \\ 1 \end{bmatrix}, b_2 =\begin{bmatrix} 2 \\ 1 \end{bmatrix}$$. Define $$T: \mathbb{R}^2 \rightarrow \mathbb{R}^2$$ by $$T(x)=Ax$$. Find the matrix for $$T$$ relative to the basis $$B$$.

Is this the same as the change of coordinates from one matrix to another? If so I have the augmented matrix $$\begin{bmatrix} 3 & 2 & 0 & 9\\ 1 & 1 & -1 & 6 \end{bmatrix}$$ which yields $$\begin{bmatrix} 1 & 0 & 2 & -3 \\ 0 & 1 & -3 & 9 \end{bmatrix}$$, so then would the matrix be $$\begin{bmatrix} 2 & -3 \\ -3 & 9 \end{bmatrix}$$? This is also a little different from other problems I've done, as some given property usually has to be satisfied.