Chapter 9.1, Problem 55E

In Problems 51-56, are there unique values of $a,b$, and $c$ that make $P$ a transition matrix? If so, complete the transition matrix and draw the corresponding transition diagram. If not, explain why.

$\begin{array}{l}\begin{array}{ccc}A& B& C\end{array}\\ P=\begin{array}{c}A\\ B\\ C\end{array}\left[\begin{array}{ccc}.2& .1& 7\\ a& .4& c\\ .5& b& .4\end{array}\right]\end{array}$