1. Why does Theorem FTMR deserve the moniker “fundamental”?
2. Find the matrix representation, $\matrixrep{T}{B}{C}$ of the linear transformation \begin{equation*} \ltdefn{T}{\complex{2}}{\complex{2}},\quad\lt{T}{\colvector{x_1\\x_2}}=\colvector{2x_1-x_2\\3x_1+2x_2} \end{equation*} relative to the bases \begin{align*} B&=\set{\colvector{2\\3},\,\colvector{-1\\2}}& C&=\set{\colvector{1\\0},\,\colvector{1\\1}} \end{align*}
3. What is the second “surprise,” and why is it surprising?