Answer
See below
Work Step by Step
Given the set of vectors $\{(2,-1),(3,2)\}$
Obtain: $\begin{vmatrix}
2 & 3\\ -1 & 2
\end{vmatrix}=4-(-3)=7 \ne 0$
Thus, the set of vectors are notcoplanar and therefore set $\{(2,-1),(3,2)\}$ does span $R^2$
Rewrite $v=(5,-7)=a(2,-1)+b(3,2)$
We have the system:
$2a+3b=5\\
-a+2b=-7$
then $2a+3b+2(-a+2b)=7b=-9\ rightarrow b=-\frac{9}{7}$
Substitute: $a=2b-7=2(-\frac{9}{7})+7=\frac{31}{7}$
Hence vector $v=(5,-7)$ can be written as a linear combination of vectors $\{\frac{31}{7}(2,-1)-\frac{9}{7}(3,2)\}$
