Question: Given two matrices and , let be the product (here we assume the dimensions of and are such that the multiplication is defined). The product

Given two matrices and , let be the product (here we assume the dimensions of and are such that the multiplication is defined). The product can be computed in two different ways: Multiplication by columns: Let and be the jth columns of the matrices and respectively. By definition of matrix-matrix multiplication, we have , i.e. each column of the matrix C is given by the product of the matrix A times the corresponding colum of the matrix B: Multiplication by rows: Let and and be the i-th rows of the matrices and respectively. By definition of matrix-matrix multiplication, we have , i.e. each row of the matrix is given by the product of corresponding row of times the matrix : In this exercise we will explore the two methods of computing the product. Two 3 3 random matrices with entries between 0 and 10 are generated for you using the commands: R =10*rand(3), S=10*rand(3) The command rand(3) generates a random 3 3 matrix with entries in between 0 and 1. We multiply that matrix by 10 so that it has entries between 0 and 10. 1. Multiplication by columns

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