Are you a Harry Potter fan? Have you read the books? Seen the movies? I love Harry Potter, and for our application problem this week, you are going to apply matrices to the field of cryptography in order solve a Harry Potter-Themed Problem! Yay! Here is your challenge---- Harry Potter is in deep trouble. He is being pursued by Lord Voldemort and is presently hiding in a secret location to escape from being captured by him. He needs to send messages to his two good friends, Ron and Hermione, to tell them about his situation and whereabouts. Of course, he has to send the messages in code, just in case they are intercepted and cracked by Lord Voldemort or other evil wizards along the way. So he composes his coded message by replacing each letter in the actual message by a number according to a certain code. Then he encrypts this coded message even further through the use of an "Encoding Matrix". He has to be extra sure that no one but Ron and Hermione have access to his message. It is your job to crack to the code below and get Harry's message to Ron and Hermione so they know that he is in trouble! His message will also tell you where he is, so his friends can go save him!Harry's Coding System: Table 1. Coding system. A B C D E F G H J K L M N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 O P Q R S T U V W X Y Z ? 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29Here is Harry's Coded Message in Linear Form: (Hint: arrange this into a Matrix by columns, so going down first, using only 3 rows) 21, -4, 22, 6, 18, 29, 1, 19, 21, 22, -17, 5, 40, -8, 59, 10, -9, 2, 22, -13, 18, 34, -14, 40, 8, -3, 5, 37, -11, 44, 20, -4, 27, 16, 5, 28, 8, 19, 35, 12, 2, 25, 27, -27, 0 Here's an Example to Get You Started with Setting up the Matrix (see how I arranged the numbers above by columns?): 21 6 1 22 40 10... -4 18 19 -17 -8 -9 ... 22 29 21 5 59 2...Here is the Decoder Matrix that Harry has sent to Ron and Hermione: 2 1 2 2 -1 -1 -1 1 HINT: You do NOT need to find the inverse of the Decoder. It is a "Decoder" for a reason - Harry sent it to be used as a tool! Be careful when you multiply! And Yes! Definitely use your calculator! When you Decode: Everything should be read by COLUMNS, so make sure you translate by going down first, then down the next column, etc. So the first three numbers in the first column are your first three letters in the message!This week, you will be applying what you have learned about matrices to the field of Cryptography! Cryptography (or Cryptology), the science of encrypting and deciphering messages written in secret codes, has played a vital role in securing information since ancient times. Julius Caesar employed what has become known as the "Caesar Shift Cipher" when encoding messages to communicate with his generals. Under this form of encryption technique, each letter in a message is substituted with the letter that was a certain number of places further down the alphabet. Caesar used a shift of three places, and so A is replaced by D, B is replaced by E, and so on. In modern history, the Nazis used the presumably highly sophisticated "Engima" machine to encrypt their messages when they communicated, still unaware that three Polish mathematicians had already cracked the unbreakable codes of the Engima machine and had provided the Allied Forces with the means to gain access to their top secrets. All thanks to Cryptography! More recently, with millions of financial transactions conducted over the Internet daily, cryptography has become more important than ever. Companies have begun to make online transactions more secure by installing encryption software to prevent sensitive information, such as credit card numbers, from falling into the wrong hands