Cryptography Question

Math 2373 Lab 2: Chapter 2 You must show ALL your work to receive full credit for each problem. Final answers must be simplified and circled. 1. Solve the following system of three equations in three unknowns by using the inverse of the matrix of coefficients. 2×1 + x 2 + 2x 3 = 3 x2 + x3 = 1 x1 + 2x 2 + 2x 3 = 4 (a) Determine the inverse of the matrix of coefficients using Gauss-Jordan elimination (row operations). You must show at least five of the resulting matrices to receive full credit. (b) Use matrix multiplication with the inverse to solve. 2. Consider the economy consisting of three industries. Determine the output levels required of each industry in each situation to meet the demands of the other industries and of the open sector. You may use your calculator to find any necessary inverses, but you must show all matrices. 0.20 0.20 0.10  4  0  8       A= 0 0.40 0.20  , D = 8  ,  8  , and 24 in turn.  0 8  16  8  0.20 0.60  (a) Find the matrix I – A. (b) Use your calculator to find the inverse of I – A. (c) Use matrix multiplication (you may use your calculator) to find X for each of the three values of D. 3. A square matrix A is defined to be idempotent if A2 = A. Prove that if matrices A and B are both idempotent and AB = BA, then AB is also idempotent. Note any theorems used to justify your work. 4. Consider the economies consisting of three industries. The output levels of the industries are given Determine the amounts available for the open sector from each industry. 0.20 0.20 A = [0.40 0.40 0.40 0.10 0 36 0.60], D = [ 0 ] 0.40 18 (a) Find the matrix I − A. (b) Use your calculator to find the inverse of the matrix you found in part (a). (c) Find X for the given values of D. 5. The following table represents information from questionnaires given to a group of people. Group Member Person whose opinion valued M1 M2 M2 M3 M3 M1 M4 M2 (a) Construct the diagraph that describes the leadership structure within the group. (b) Construct the distance matrix for the group. (c) Rank the members from most influential to least influential.