1. Cryptopgraphy (a) We wish to encode a message using a simple cipher and matrix multiplication. For the cipher, we will assign to the letters of the alphabet A B C ... Z the numbers 1,..., 26 corresponding to their position in the alphabet and the number 27 represents a blank space. The idea is to write the message as a m x nmatrix and then use an invertible mxm matrix and matrix multiplication to encode and decode the message. For example, we may write "PEACE" as the 2 x 3 matrix M by using the cipher and then grouping the numbers into 2 x 1 columns, thus M = 16 1 5 5 3 27 If we now take a 2 x 2 invertible matrix E as the encryption matrix, we may encrypt the message using matrix multiplication as EM. For example, if E= the message "PEACE", after the multiplication EM and 'unzipped' from the matrix becomes 54 53 - 26 - 34 42 The following message was encrypted using the matrix C where: 1 2 3 C 2 5 3 108 107 193 133 108 183 156 76 91 177 136 236 187 95 172 118 Decode this message. You can use software or a site such as matrixcalc.org to perform the calcula- tions, but you must clearly show your procedure. (b) Spy Headquarters sends a message to one of its agents using the encoding matrix The agent uses the matrix A = B = -(3) 3 5 (14) to send messages to their informers. Find the encoding matrix that is consistent with this commu- nication pathway that enable Headquarters to send messages directly to the informers. Show all of your work. 1. Cryptopgraphy (a) We wish to encode a message using a simple cipher and matrix multiplication. For the cipher, we will assign to the letters of the alphabet A B C ... Z the numbers 1,..., 26 corresponding to their position in the alphabet and the number 27 represents a blank space. The idea is to write the message as a m x nmatrix and then use an invertible mxm matrix and matrix multiplication to encode and decode the message. For example, we may write "PEACE" as the 2 x 3 matrix M by using the cipher and then grouping the numbers into 2 x 1 columns, thus M = 16 1 5 5 3 27 If we now take a 2 x 2 invertible matrix E as the encryption matrix, we may encrypt the message using matrix multiplication as EM. For example, if E= the message "PEACE", after the multiplication EM and 'unzipped' from the matrix becomes 54 53 - 26 - 34 42 The following message was encrypted using the matrix C where: 1 2 3 C 2 5 3 108 107 193 133 108 183 156 76 91 177 136 236 187 95 172 118 Decode this message. You can use software or a site such as matrixcalc.org to perform the calcula- tions, but you must clearly show your procedure. (b) Spy Headquarters sends a message to one of its agents using the encoding matrix The agent uses the matrix A = B = -(3) 3 5 (14) to send messages to their informers. Find the encoding matrix that is consistent with this commu- nication pathway that enable Headquarters to send messages directly to the informers. Show all of your work.