1. Demonstrate how to use Excel to solve a system of linear equations using matrices. 2. Demonstrate how to use Excel to encrypt or code a message using matrices and their inverse. 3. Demonstrate how to use Excel to add and multiply matrices. Each of the following 3 topics must be addressed: 1. Demonstrate how to use Excel to solve a system of linear equations using matrices. Example: Joe has $3.30 in his pocket, made up of nickels, dimes, and quarters. There are 30 coins, and there are five times as many dimes as quarters. How many coins of each type does he have? 2. Demonstrate how to use Excel to encrypt or code a message using matrices and their inverse. Example: The message to be encoded is SEPTEBMER IS HERE The encoded message to be formed using triplets of numbers and the 33 matrix A=132010051 whose inverse is A1=1132010051 Use the following association of letters and divide the message into triplets of letters: SEP TEM BER ISH ERE Now multiply the matrix A times each column vector of the message. You will receive the coded message. To decode the message, form 31 column vectors of the numbers in the coded message and multiply on the left by A1. 3. Demonstrate how to use Excel to add and multiply matrices to prove the following properties of matrices a. Cumulative property for addition: A+B=B+A b. Associative property for addition: A+B+C=A+B+C c. Associative property of matrix multiplication ABC=ABC d. Distributive property of matrix multiplication AB+C=AB+AC e. Identity property InA=A and AIn=A