7. (e) (2 points) Please answer TRUE or FALSE and give a CONCISE explanation: In the graph represented by the adjacency matrix

$\begin{array}{c|ccccccc} & e_1 & e_2 & e_3 & e_4 & e_5 & e_6 & e_7 \\ \hline v_1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ v_2 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ v_3 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ v_4 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ v_5 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \end{array}$

with $|e_1|=1$, $|e_2|=2$, $|e_3|=1$, $|e_4|=4$, $|e_5|=1$, $|e_6|=4$, $|e_7|=5$, there exists an Euler path from $v_5$ to $v_1$.