計算機數學

(4分) Let $E = \{v_1,v_2\} = \left\{\begin{bmatrix}3\\7\end{bmatrix}, \begin{bmatrix}5\\14\end{bmatrix}\right\}$ and $F = \{u_1,u_2\} = \left\{\begin{bmatrix}2\\5\end{bmatrix}, \begin{bmatrix}1\\3\end{bmatrix}\right\}$ be two bases for $\mathbb{R}^2$.

If $[I]_E^F = \begin{bmatrix}a & b\\ c & d\end{bmatrix}$ is the transition matrix from $E$ to $F$, where $a,b,c,d \in \mathbb{R}$. Please determine the value of $a+b+c+d$.