One of my favorite applications of matrices is encryption (secret codes!). Encryption is hugely useful in todayls world. It keeps our credit cards safe when we shop online, it lets top-ranking government ofcials talk to each other without being spied on by enemies, and it protects our computers from catching viruses. Matrix encryption is a simple way to encode and decode secret messages. In this project, you'll be trying to pass a message to your friend to organize where to meet when you ditch your math class. This is how matrix encryption works: 0 You will have a square matrix called the encryption key, called matrix C. The bigger the matrix5 the harder your code is to crack. For this project; we will use a 3x3. 0 Assign each letter of the alphabet a different number. Usually you'll do A=1, B=2, 0:3, etc, but you can do anything. I Put the numbers in your code into a matrix that can be multiplied by your encryption key. Fill in any blank spaces with zerOs. This is matrix A. a To encode the message: multiply the key by your numbers. The encoded message is matrix 2'. 80, Z = C-A. Remember that order matters when you multiply matrices! a To decode the message: multiply the encoded matrix by the inverse of the key. In other words, A = 01 - Z. Remember that order matters! In this project, you will choose a location to meet your friend when you ditch math class. You have previously talked about the following locations: 0 The movies I The mall a The park a Your house You were about to tell your friend where to meet you, but you didn't get a chance because a teacher was walking by! Instead, you hand your friend your encryption key matrix. In the next class, you encode your message and pass it to your friend when you switch classes. If your friend can decode your message and gure out which location you're going to, you win! But if your friend decodes the message and just gets gibberish, then you have to go to math class. 1. You and your friend create your encryption key matrix, C, together, so that you can both use it. You choose the matrix below. 'What kind of matrix is this? 3 2 1 C: 7 2 1 3 4 3 2. Together, you and your friend assign each letter of the alphabet a different number. To make it challenging, you decide to randomize the numbers as shown below. A B C E F G H I J K L M 15 10 l 8 19 3 14 20 6 12 26 17 m- 21 11 16 22 9 18 7 23 2 24 13 25 Use this list to write your message in numbers below. It should say the location of where you want to meet. Use zeros for empty spaces (between words and at the end if there is extra room). 6181-35-5 3. Write the numbers from step 2 as a matrix. This is matrix A, the preencoded mes- sage. It should have only three rows so that you can multiply C by it. Use as many columns as you need. 4. Encode your message. That is, nd matrix Z, knowing that Z = C - A. You give this matrix to your friend. At this point I will decode your message to see what location you've chosen. 5. Your friend responds to your message, saying the following: 72 60 6 6218 716912108 90 84118 18109 412812 40 36 18 96 45 39 12 Write this as a matrix that can be multiplied by your key C (it should have only three rows). This will be matrix Z. 6. In order to decode your friend's message, you'll need the inverse of the key. Find 01. 7. You can nd the plain numbers matrix, A, of your friends; message by multiplying C'l - Z. Find A. 8. What did your friend's message say