FBI Statement: On a mid-summer morning, the dew fell across Washington, D.C. The city seemed to be quiet but maybe it wa

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FBI Statement: On a mid-summer morning, the dew fell across Washington, D.C. The city seemed to be quiet but maybe it was too quiet. The Washington Monument stands as the watch guard for the city that contains the most precious nationali treasures, but the best security in the world had no match early this morning. At the National Archives, the United States' most treasured documents, The Charters of Freedom (Declaration of Independence, Constitution, and Bill of Rights) were stolen on July 15th. If the documents are not found, then they could be sold for millions of dollars on the black market and destroyed! The Federal Bureau of Investigation (FBI) needs the assistance of any person with good matrix knowledge, and you meet the criteria. The thief is named Euclid Descartes, and he has left clues to find the Charters of Freedom. Break each clue that Euclid has left for a zip code which gives the location of the Charters of Freedom... The activity will be completed following these steps: INITIAL POST= Steps 1-6 FINAL POST= Steps 7-8 + Bonus I Step 1: Solve each of the five clues provided. Each clue results in a single value. These clues can be solved using what you have learned in Modules 1 & 2. Step 2: The values found will create a 5-digit zip code. Use the statements provided by Euclid to determine which slot in the zip code each value should be placed. Step 3: Determine the encoding 2x2 matrix by reading through Euclid's final statement. Step 4: Watch the video on how to use the encoding matrix to break the cypher. Step 5: Create your own encoded message sharing what you will bring to the party celebrating the return of the Charters of Freedom. Step 6: Report your findings and your encoded message to the class. Step 7: Respond to a classmate by solving their encoded message. Step 8: Check to see if the decoding of your message by a classmate is correct.
Step #1 - Solve the Clues Use the clues below to determine a single value solution. Once you have a value for each clue, proceed to Step #2. Clue #1: Row operations are an exciting way to begin! Perform the row operation -3R + R₂ → R, on 2 4 3] 1 61. The entry in the (3,2) position is the solution. Find me! -1-96 the matrix 8 Clue #2: I had to scale across the Chesapeake Bay just to find my way away from the city. Consider the 10-12 15 Find the scalar value, w, that makes this equation true. matrix equation w 3 8 The DENOMINATOR of this scalar is the solution. Find me! Clue #3: 12 3 -3 2 -9 6 All the entries of M² 10 -6 4 5 My favorite matrices are nilpotent! Suppose that: M = 15 (M x M) are the same and that number is the solution. Find me!
matrix equation w 3 Clue #3: 12 3 8 2 The DENOMINATOR of this scalar is the solution. Find me! Find the scalar value, w, that makes this equation true. 5 My favorite matrices are nilpotent! Suppose that: M = 15 -3 2 -9 6 All the entries of M² 10 -6 4 Clue #5: I (M x M) are the same and that number is the solution. Find me! Clue #4: I love matrix multiplication. Suppose I have a 3x4 matrix. The number of rows in the second matrix that will allow me to multiply the matrices is the solution. Find me!" 3 11 10 11 The Not every matrix has an inverse, but this one sure does. Let T = 75 15 88 44 NUMERATOR of the entry in the (1,2) position of T-¹ will be the solution. Find me!
Step #2 - Find the Zip Code I made it to an island in the Chesapeake Bay, but do not try guessing because there are over 200 islands in the bay. If you have all the solutions and you order them correctly, then you will find the zip code of my location. For the value found in clue #1, Euclid states, "The zip code will be a five-digit code. The solution to this clue will be on an even slot of the five-digit code." For the value found in clue #2, Euclid states, "The zip code will be a five-digit code. The solution to this clue will be a perfect square slot of the five-digit code." For the value found in clue #3, "The zip code will be a five-digit code. The solution to this clue will be either the first or the last slot of the five digit-code." For the value found in clue #4, Euclid states, "The zip code will be a five-digit code. The solution. to this clue will be either the third or the fifth slot of the five digit-code." For the value found in clue #5, Euclid states, "The zip code will be a five-digit code. The solution. to this clue will be the fourth slot of the five-digit code."
Download and open the document below to reveal the Clues: Step #1: The Clues Download and open the document to find out how to use the clue answers to find the zip code: Step #2: Zip Code I Download and open the document below to decode the message: Step #3 & 4 FBI Statement: Excellent work determining Euclid's zip code. We are so close to finding the Charters of Freedom, but we still need assistance. Matrix algebra has been used for decoding messages for centuries, and Euclid has encoded a message to us. Thankfully, Euclid made a mistake and gave us his encoding matrix (this is the matrix that jumbles up his message). We need lead experts in linear algebra to break Euclid's code. Step #5 - Create your own Coded Message : ⠀ ***
Step #5 - Create your own Coded Message Congratulations! Hopefully, your location is correct! To celebrate finding the Charters of Freedom, the FBI is throwing a party! Everyone involved in the case is going to bring their favorite party dish to share. Create your own 2x2 or 3x3 encoding matrix and let everyone know what you are bringing to the party in a coded message!! Decide on your dish and then code it using the same method used to solve the prior message. Step #6 - Share your Findings & your Coded Message 1-Post your findings and coded message on the discussion board. You must post the location of the Charter of Freedom by giving the specific location message you decoded and the Zip Code. 2-Post the coded message of what dish you will bring to the party along with the encoding matrix. (Note: you will not see anyone's posts until you have posted) I Here is an example of what a post might look like: The Charters of Freedom are located at: Fort Knox, 40121 I am bringing to the party: 163 272 122 120 201 77 119 126 88 161 250 112 197 295 137 My 3 x 3 encoding matrix is: 235 186 124
The Charters of Freedom are located at: Fort Knox, 40121 1 am bringing to the party: 163 272 122 120 201 77 119 126 88 161 250 112 197 295 137 My 3 x 3 encoding matrix is: 235 186 124 Step #7 - Respond to a Classmate I Find a classmate with NO responses and decode their message. Respond to their post with what their message says. Step #8 - Watch for Posts and Respond Once a classmate has decoded your message, respond to them by letting them know if they are correct or not. Bonus Step for Extra Credit: Decode what I am bringing to the party from my example post above and include that in your first post. Grading Notes: • You may re-post if you have an error, but you MUST provide an explanation of what your error was, how you discovered your error, and how you fixed the error. Re-posts without explanation will not be considered when grading the activity. .DO NOT DELETE or MODIFY ORIGINAL POSTS! Deleted or modified posts will result in a loss of points on the activity. Use the guidelines above to re-post and fix errors.
Step #3 - Find the Encoding Matrix Euclid says, "I was always 1st place in every math competition, so you will never break my code. 2-years ago I was told my proof to the Riemann Hypothesis was wrong, and I was furious; so, I enjoy causing some trouble using mathematics now! I stole the Charters of Freedom in 1 try, and there is 0 (zero) chance you will find them. My encoding message is a 2 x 2 matrix found in this message. If you are bold enough to continue trying, know that the (1,2) and (2,1) positions are the same value. Below is the location of the Charters of Freedom combined with the zip code you may have found earlier. Good luck never finding your precious Charters of Freedom!" Location: 47, 23, 45, 20, 49, 18, 16, 1, 38, 19, 25, 8, 13, 4, 25, 1, 27, 1 Step #4 - Learn How to Crack the Code Before breaking the code, watch the following video on Hill Ciphers and code breaking: or review Section 4.5 in your text on Cryptography! Number Substitution Cypher D AINH А 1 B 2 Space 0 05 14 15 с 3 P 16 1640 17 ESR8 5 6699 6149 G 7 T 18 19 20 H&U 8 21 I 946 V J 10 W 22 23 Location of Charters of Freedom (Message + Zip Code Location): K 11 L 12 X Y 24 25 M 13. Z 26