1. Let A and B be the following matrices: 1 3 A_ (i g 1) L? 1 2 0 1 For each of the following expmssions, rst state whether or not they can be calculated. If they can be calculated, nd them. Show your working. (a) AB (b) A B'f' 68 4 64 73 2. Matrix C is a coded message where C= 61 4 52 51 CTO 109 5 120 170 You know that each letter of the original message was first replaced with the number corresponding to its placement in the English alphabet (eg. E was replaced with 5) and any spaces in the message were replaced with zeroes. Then the message was encoded by multiplying 2 3 the message matrix, M, on the left by the coding matrix, A = 0 1 4 such that AM = C 5 6 0 (or Coding matrix x Message matrix = Coded Message matrix) (a) Decode the message using your knowledge of matrices to find out what it says? (If you do this correctly you will end up with a message in Te Rao Maori that means " You are doing well"!) (b) For each of the matrices B, C and D given below, state whether it could be used to encode the message "KAUA E HEMO" (which means "Don't give up" ), explaining your answer. 5 6 6 8 K A U 2 2 8 A OE i. BM = 6 6 2 8 HE 2 3 6 M 0 0 K U A ii. CM = 3 5 1 2 OEOH EMO 0 iii. DM - (2 3) (6 AUAOE HEMO 0