make algorithm  for MatrixMultiplication (A1, A2, ... , An)  pre-cond: An instance is a sequence of n matrices.  post-cond: optSol is a bracketing that requires the fewest multiplications, and optCost is the resulting number of multiplications.

Rank and Nullity This activity shall determine the rank and nullity of a matrix. Create a function that will be able to solve the following: a. accept the a rectangular array of elements. b. compute the rank c. compute for the nullity of the matrix d. identify the rowspace of A e. identify the column space of A. Refer to the discussion item at the MATLAB Discussion handout. [Rank, Nullity, Rowspace, Nullspace] = ranknullity(A)

Create a 3-by-3 matrix: A = [1 2 3;4 5 6;7 8 10] (a)Extract a submatrix B consisting of rows 1 and 3 and columns 1 and 2 of the matrix A (b)Interchange rows 1 and 3 of A and put it in a variable C. Hint: use the vector of row indices together with the colon operator (c)Create a vector version of the original matrix A. (d)Delete the 2nd column of the original matrix A and put it in a variable called A. (e)Insert a 2nd column to the new matrix A to restore it back to its original form A. (f) Extract those entries of the original matrix A that are greater than 5

Find a sorted matrix: The input is a real number x and a matrix A[1..n, 1..m] of nm real numbers, with each row A[i, 1..m] and column A[1..n, j] sorted. The objective is to locate the largest array entry A[i, j] that is less than or equal to x, or to report that all components of A are greater than x. Create and test an iterative method that analyses as few matrix elements as feasible. Be cautious if you assume a simple binary search would fix the problem. Find a sorted matrix: The input is a real number x and a matrix A[1..n, 1..m] of nm real numbers, with each row A[i, 1..m] and column A[1..n, j] sorted. The objective is to locate the largest array entry A[i, j] that is less than or equal to x, or to report that all components of A are greater than x. Create and test an iterative method that analyses as few matrix elements as feasible. Be cautious if you assume a simple binary search would fix the problem.