Please answer with full details for full credit: Knowing that a 2x2 matrix is en
ID: 2943214 • Letter: P
Question
Please answer with full details for full credit:
Knowing that a 2x2 matrix is encoded by post-multiplying it by the encoder matrix (3 1 5 2), decode the following message: E A U Z J V W WW E A O R U F Q E X L W K S S K F G L W This method does have its limitations. Using the encoding matrix from above and pre-multiplying, encode the word HELP. Now decode the result to get back to HELP. This is fairy simple. Now, using the encoding matrix (4 7 6 5) and pre-multiplying, encode the word HELP. Now try to decode the message. This does not give an appropriate result. (M&P;) Investigate your result and provide the limitation(s) that needs to be applied to the encoding matrix. Note: There are methods available to overcome some of these limitations. However, for this assignment we will use the method shown in the assignment.Explanation / Answer
Question really needs clarity. Check if the below is of any help for you. ENCODING Step 1 Choose a message. example: MATH ROCKS Step 2 Replace the letters with numbers using A = 1, B = 2, C = 3, etc. A space in between words is assigned 0. MATH ROCKS would become: 13 01 20 08 00 18 15 03 11 19 Step 3 Place the numbers in a “2 x c” matrix, since there are 10 coded letters, you use a 2 x 5 matrix: [13 20 00 15 11] [01 08 18 03 19] Step 4 Make up a 2 x 2 matrix to use as the encoding matrix. Make sure your matrix does NOT have a determinant of zero (why?). I’ll use this matrix, which has a determinant of 10: [ 4 -1] [ 2 2] Step 5 Multiply the numbered message by the encoding matrix, the result is a code! [4 -1] [13 20 00 15 11] [51 72 -18 57 25] [2 2] [01 08 18 03 19] equals [28 56 36 36 60] The string of digits 5172-1857252856363660 can be sent to someone and decoded. DECODING Step 1 Place the string of digits, two at a time, in a 2 x c matrix. Step 2 Multiply the ENCODED message by the INVERSE OF THE CODING MATRIX to obtain the DECODED message. In our example, we would multiply the encoded matrix by: [ 0.2 0.1] [ -0.2 0.4 ] to obtain the original set of numbers that represent the phrase: MATH ROCKS You practice it: 1. Change the letters of the phrase: “Union is number one” to numbers using the alphabet number system described above: Put the numbers in a 2 x 10 matrix. 2. Encode the message by multiplying the message matrix by the encoding matrix below: [ 3 -1] [ -5 2 ] 3. find the inverse of the encoding matrix. 4. Multiply the encoded message by the inverse. If you did it right, you should end up with the numbers that correspond to the original message: Union is number one