Handwritten solution please

Problem 3. Read section 15.2 in the book and answer the following questions: 1. What is the matrix chain multiplication problem? Describe it in your own words. 2. What are the different ways of parenthesizing the matrix product A1 A2 A3 A4? 3. How many scalar multiplications are needed to compute the product, for each of the different paran- thesizations, assuming the matrix dimensions are 10 100, 100 x 7, 7 x 100, and 100 50 respectively? 4. How long would it take to try all possible parenthesizations for a chain of n matrices? State an asymptotic lower bound (as tight as possible), assuming that two numbers of arbitrary length can be multiplied in constant time. 5. What is the runtime of the dynamic programming algorithm? 6, why does the d.. algorithm need a two-dimensional array to store the subproblem solutions? 7, How does the d.. algorithm ensure that solutions to subproblems are computed in the correct order so they are available when they are needed