$[20$ points total$]$

a$)[15$ points$]$ Suppose you are trying to solve the matrix chain problem with four matrices with dimensions as shown below.

$\backslash$table$[[$A$,$B$,,$C$,$x$,,],[$x$5,5$x$4,,4$x$3,,,]]$

Using the dynamic programming method for this problem from class, make solution tables M and P $.$ Be sure to show your work showing how you obtained these answers.

b$)[5$ points$]$ Show the final parenthesization of the matrix chain that results in the fewest multiplications for this problem. You must also circle the entries in the $P$ table which you use in your backtracking to obtain the solution.