Performing the indicated operations (Definition CVA, Definition CVSM), we obtain the vector equations
\begin{align*}
\colvector{3\\2}
&=\alpha\colvector{1\\0} + \beta\colvector{0\\1}
=\colvector{\alpha + 0 \\ 0 + \beta}
=\colvector{\alpha\\ \beta}
\end{align*}
Since the entries of the vectors must be equal by Definition CVE, we have $\alpha = 3$ and $\beta = 2$.