Let a, b and c be positive real numbers,
$$\left[ \begin{array} { l l }
a & b \\
0 & c
\end{array} \right] \cdot \left[ \begin{array} { l l }
a & b \\
0 & c
\end{array} \right] = \left[ \begin{array} { l l }
1 & 2 \\
0 & 4
\end{array} \right]$$
The matrix equation is given. Accordingly, what is the sum $a + b + c$?
A) $\frac { 11 } { 3 }$\\
B) $\frac { 7 } { 4 }$\\
C) 4\\
D) 5\\
E) 6