Question 1, 2 And 3 A = [ 2 5 ] is the given matrix. ...
Question 1, 2 And 3
A = [ 2 5 ] is the given matrix.
[ 3 5 ]
1) (2marks) encode the message "TEST".
2)(2marks) find the inverse of A. Note that your matrix entries should be integers in the range 0,...25.
3) (2marks) use your answer above to decode the message "ETAJ"
Homework Answers
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- -5 3 a. Use the coding matrix A = to encode the word TOYS. 0...
- -5 3 a. Use the coding matrix A = to encode the word TOYS. 0 2 1 3 5 10 b. Use its inverse, A to decode 25, 30, -24, 24. 1 O 2 Evaluate the determinant. 28 3 7
1 5 a. Use the coding matrix A = to encode the word SELL. - 52...
1 5 a. Use the coding matrix A = to encode the word SELL. - 52 2 5 -- 27 27 b. Use its inverse, A-1 = to decode 79, 10, 93, -87. 9 5 LO 1 27 27 a. The encoded message is (Type the values in the correct order, separated by commas.) b. The decoded message is (Type the word.)
Matrices are used to encode and decode encrypted 6: Matrices and Cryptography messages. Using the following code, T...
Matrices are used to encode and decode encrypted 6: Matrices and Cryptography messages. Using the following code, Task KİLİMİN | SPACE |-Z --T-T-u一ㄒㄧˇ-ㄒㄧ-w-ㄒㄧㄨㄧㄧㄧㄚ s116 17 18 19 20 21 22 23 24 25 26 The sentence MATRICES ARE FUN becomes: FİUİN AİRİE 0161211 14 9L3151 1910|111813 a. To encode the message, multiply by an invertible matrix A. Write the coded message in a 3x6 matrix, adding 0's for blanks. Calculate the product using a graphing calculator. [7-3-31「13 18 5 1...
Activity 15 - Matrices, Sequences and Conics Math 180 Task 6: Matrices and Cryptography messages. Using the followi...
Activity 15 - Matrices, Sequences and Conics Math 180 Task 6: Matrices and Cryptography messages. Using the following code, Matrices are used to encode and decode encrypted KİLİMİN 2 | 3 | 4 | 5 | 6 17 18 T-9 10111 | 12 | 13 | 14 一0一ㄧ一Pー1_Qー1.RT-s-T_T-I-U 15 16 17 18 19 20 21 ㄨㄧㄒㄧㄚ 1-2.TSPACE 24 25 26 ˇ一ㄒ一w 22 23 The sentence MATRICES ARE FUN becomes: AİRİE 13 1 20 189 3 5 19 0 1 18...
a. b. c. What does the ciphertext ONL decode to with the modular inverse matrix from Question b? d. We use an encoded...
a.
b.
c. What does the ciphertext ONL decode to with the modular
inverse matrix from Question b?
d. We use an encoded text using a Caesar cipher. The ciphertext
was intercepted which is: THUBYLDH. What is the word? How did you
work this out?
Encode the uppercase letters of the English alphabet as A-0, B-1, C-2 and so on. Encrypt the word BUG with the block cipher matrix 16 4 11] 10 3 2 using modulo arithmetic with modulus...
You are wanting to communicate secret messages with your friend, and you choose to do this with matrices. The encoding matrix that you choose to use is 2 -2 -1 6 You use the following key to convert...
You are wanting to communicate secret messages with your friend, and you choose to do this with matrices. The encoding matrix that you choose to use is 2 -2 -1 6 You use the following key to convert your message into a string of numbers, where "O" is used as a placeholder where required. A B C D EF G H IJ K L M 10 2 11 24 19 5 25 20 3 7 16 6 14 N O...
68 4 64 73 1 5. Matrix C is a coded message where C61 4 52 51 0 109 5 120 170 5 You know that each letter of the original message was first replaced with the number corresponding to its placement in...
68 4 64 73 1 5. Matrix C is a coded message where C61 4 52 51 0 109 5 120 170 5 You know that each letter of the original message was first replaced with the number corresponding to its placement in the English alphabet (eg. E was replaced with 5) and any spaces in the message were replaced with zeroes. Then the message was encoded by multiplying the message matrix, M, on the left by the coding matrix,...
Please answer question 3 Find all (infinitely many) solutions of the system of congruence's: Use Fermata...
Please answer question 3
Find all (infinitely many) solutions of the system of congruence's: Use Fermata little theorem to find 8^223 mod 11. (You are not allowed to use modular exponentiation.) Show that if p f a, then a^y-2 is an inverse of a modulo p. Use this observation to compute an inverse 2 modulo 7. What is the decryption function for an affine cipher if the encryption function is 13x + 17 (mod 26)? Encode and then decode the...
5. Create a 4 x 4 matrix , called A, of randonm integers between 1 and 10. 1. find the transpose of A 2. find the trace of A 3. find the inverse of A 5. Create a 4 x 4 matrix , called A, of...
5. Create a 4 x 4 matrix , called A, of randonm integers between 1 and 10. 1. find the transpose of A 2. find the trace of A 3. find the inverse of A
5. Create a 4 x 4 matrix , called A, of randonm integers between 1 and 10. 1. find the transpose of A 2. find the trace of A 3. find the inverse of A
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eige...
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eigenvalues and determine the determinant, (c) Compute the corresponding eigenvectors of the matrix above (a) Show that the matrix is positive definite. 1 | so that the characteristic polynomial 5 marks 0 (d) Choose a, band c in the matrix B = | 0 Based on Cayley-Hamilton's theorem, every matrix fulfills its characteristic polynomial, using the...
- -5 3 a. Use the coding matrix A = to encode the word TOYS. 0 2 1 3 5 10 b. Use its inverse, A to decode 25, 30, -24, 24. 1 O 2 Evaluate the determinant. 28 3 7
1 5 a. Use the coding matrix A = to encode the word SELL. - 52 2 5 -- 27 27 b. Use its inverse, A-1 = to decode 79, 10, 93, -87. 9 5 LO 1 27 27 a. The encoded message is (Type the values in the correct order, separated by commas.) b. The decoded message is (Type the word.)
Matrices are used to encode and decode encrypted 6: Matrices and Cryptography messages. Using the following code, Task KİLİMİN | SPACE |-Z --T-T-u一ㄒㄧˇ-ㄒㄧ-w-ㄒㄧㄨㄧㄧㄧㄚ s116 17 18 19 20 21 22 23 24 25 26 The sentence MATRICES ARE FUN becomes: FİUİN AİRİE 0161211 14 9L3151 1910|111813 a. To encode the message, multiply by an invertible matrix A. Write the coded message in a 3x6 matrix, adding 0's for blanks. Calculate the product using a graphing calculator. [7-3-31「13 18 5 1...
Activity 15 - Matrices, Sequences and Conics Math 180 Task 6: Matrices and Cryptography messages. Using the following code, Matrices are used to encode and decode encrypted KİLİMİN 2 | 3 | 4 | 5 | 6 17 18 T-9 10111 | 12 | 13 | 14 一0一ㄧ一Pー1_Qー1.RT-s-T_T-I-U 15 16 17 18 19 20 21 ㄨㄧㄒㄧㄚ 1-2.TSPACE 24 25 26 ˇ一ㄒ一w 22 23 The sentence MATRICES ARE FUN becomes: AİRİE 13 1 20 189 3 5 19 0 1 18...
a.
b.
c. What does the ciphertext ONL decode to with the modular
inverse matrix from Question b?
d. We use an encoded text using a Caesar cipher. The ciphertext
was intercepted which is: THUBYLDH. What is the word? How did you
work this out?
Encode the uppercase letters of the English alphabet as A-0, B-1, C-2 and so on. Encrypt the word BUG with the block cipher matrix 16 4 11] 10 3 2 using modulo arithmetic with modulus...
You are wanting to communicate secret messages with your friend, and you choose to do this with matrices. The encoding matrix that you choose to use is 2 -2 -1 6 You use the following key to convert your message into a string of numbers, where "O" is used as a placeholder where required. A B C D EF G H IJ K L M 10 2 11 24 19 5 25 20 3 7 16 6 14 N O...
68 4 64 73 1 5. Matrix C is a coded message where C61 4 52 51 0 109 5 120 170 5 You know that each letter of the original message was first replaced with the number corresponding to its placement in the English alphabet (eg. E was replaced with 5) and any spaces in the message were replaced with zeroes. Then the message was encoded by multiplying the message matrix, M, on the left by the coding matrix,...
Please answer question 3
Find all (infinitely many) solutions of the system of congruence's: Use Fermata little theorem to find 8^223 mod 11. (You are not allowed to use modular exponentiation.) Show that if p f a, then a^y-2 is an inverse of a modulo p. Use this observation to compute an inverse 2 modulo 7. What is the decryption function for an affine cipher if the encryption function is 13x + 17 (mod 26)? Encode and then decode the...
5. Create a 4 x 4 matrix , called A, of randonm integers between 1 and 10. 1. find the transpose of A 2. find the trace of A 3. find the inverse of A
5. Create a 4 x 4 matrix , called A, of randonm integers between 1 and 10. 1. find the transpose of A 2. find the trace of A 3. find the inverse of A
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eigenvalues and determine the determinant, (c) Compute the corresponding eigenvectors of the matrix above (a) Show that the matrix is positive definite. 1 | so that the characteristic polynomial 5 marks 0 (d) Choose a, band c in the matrix B = | 0 Based on Cayley-Hamilton's theorem, every matrix fulfills its characteristic polynomial, using the...
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