Task
Let's Break the Code!
You and your group member will become code breakers and able to break the code and get the message using inverse matrix. You will also be able to send messages to other groups and their members.
Here are a few things that you need to remember before you could do this project.
In this project, you and your group member have to encode and decode messages using inverse matrices.
Before you do anything, you should Convert the message to numbers (1 x 2 uncoded row matrices)
Here is an example on how to convert a message.
Steps to Encode the message:
- Write down the message to encode and substitute the space with "_".
- Write them down in uncoded form and pair them up as a row of uncoded matrices.
- Multiply each of the uncoded row with the matrix that you have chosen.
- Write down the answer (coded row matrix) using comma (,) as a coded message.
Example:
Message : Got Milk
G O T _ M I L K
[7 15][20 0][13 9][12 11]
Uncoded row matrices: [7 15] [20 0] [13 9] [12 11]
2 3
Choose a matrix: A = [ -1 1 ]
Multiply each uncoded row with the matrix A:
Uncoded Row Matrix X Encoding Matrix A = Coded Row Matrix
Coded Row Matrices: [29 6] [40 60] [35 30] [35 22]
Coded Message: 29, 6, 40, 60, 35, 30, 35, 22
Steps to Decode a Message:
- Find the inverse of the matrix that have used to encode the message
- Multiply each coded row with the inverse matrix to obtain uncoded row matrices
- Write down the uncoded row matrices
- Write down the corresponding letters
Example: Suppose we have a coded message 29, 6, 40, 60, 35, 30, 35, 22 which use the matrix A from the above example.
1 -3
1/6 -1/2
Inverse of A = 1 / (2 - (-3)) [ 1 2 ] = [ 1/6 1/3 ]
Multipy to obtain uncoded row matrices:
Coded Row Matrix X Decoding Matrix (Inverse of A or Inverse matrix) = Uncoded Row Matrix
Uncoded Row Matrices: [7 15] [20 0] [13 9] [12 11]
Message: G O T _ M I L K
Now that you have the basic knowlegde on how to convert, encode and decode a message, this is the time to become breakers and do the following tasks.
Task # 1: Name your group Choose one of the famous mathematicians as your group name. Write the name of your group with coded message using encoding method and submit it to me.
Task # 2: History Write a brief summary about the name that your group choose by doing a research on the web. Make sure to include one of his or her works.
Task # 3: Presentation Create a powerpoint presentation for your mathematician and present it to the class.