Vectors vec$(u_1)=\left[\begin{array}{cc}2& 1\end{array}\right]$ and vec$(u_2)=\left[\begin{array}{cc}3& 1\end{array}\right]$ form a basis of $R^2.$

a$)$ Show the set $\{vec(u_1),$vec$(u_2)\}$ is linearly independent.

b$)$ Find the coordinates of the vector vec$(v)=\left[\begin{array}{cc}7& 4\end{array}\right]$ with respect to the basis of vec$(u_1),$vec$(u_2)$