計算機數學

(4分) If the following matrix equation holds:

$\begin{bmatrix}1 & 0 & 0\\ a & 1 & 0\\ b & c & 1\end{bmatrix}\begin{bmatrix}1 & d & e\\ 0 & 1 & f\\ 0 & 0 & 1\end{bmatrix}=\begin{bmatrix}1 & 0 & 7\\ 0 & 1 & 2\\ -2 & 5 & 3\end{bmatrix}$

Please determine the value of $a+b+c+d+e+f$.