Apply the dynamic programming algorithm for matrix chain multiplication on the following instance: M $=$ M$1$ x M$2$ x M$3,$ where the sizes of the matrices M$1,$ M$2,$ M$3$ are respectively $20$ x $5,5$ x $50,50$ x $2.$

SHOW THE DETAILS OF YOUR CALCULATIONS IN ANSWERING THE FOLLOWING FOR THE ABOVE PROBLEM INSTANCE:

a$)[4$ pts$]$ Show the contents of the cost matrix m$.$

b$)[1$ pt$]$ What is the minimum cost of computing M$1$ x M$2$ x M$3?$

c$)[1$ pt$]$ Show explicitly where the parentheses are placed in computing M$1$ x M$2$ x M$3$ in order to achieve the minimum total cost in part $($b$)?$