Any help on this linear transformation question is very much appreciated.
Let $V$ denote the real vector space $R^2$ and $\psi : V \rightarrow V$ be a real linear transformation such that $\psi ((1, 0)) = (11, 8)$ and $\psi ((0, 1)) = (4, 3)$. Express the image $\psi ((x, y))$ of $(x, y)$ in terms of $x$ and $y$. Assume that $w_1 = (4, 5)$ and $w_2 = (9,11)$ form an ordered basis $B$ for $V$ . Working from the denition determine the matrix $M^B_B (\psi)$ with respect to the basis $B$.
does $ M^B_B(\psi)= \begin{bmatrix} -469 & -1048 \\ 388 & 867 \end{bmatrix}$ ?
thanks in advance for any help