Answered: Problem 6: Consider these two matrices:…

Problem 6: Consider these two matrices: 1 3 1 2 4 1 3 5 0 1 3 and 2 4 Assume they are used for an encryption in Hill ciphers. In each case, find two plaintexts that encrypt to the same ciphertext.

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter6: Quadratic Equations And Inequalities

Section6.6: Quadratic And Other Nonlinear Inequalities

Problem 62PS

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Question

Problem 6: Consider these two matrices:
1 3 1
1 3
and
2 4 1
2 4
3 5 0
Assume they are used for an encryption in Hill ciphers. In each case, find two plaintexts that encrypt to
the same ciphertext.

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Suppose that a message is encrypted using a Hill Cipher with matrix 1 A -1 2 If the message begins with the word "face" then what are the first four numbers of the encrypted message? Recall that we convert letters to numbers using a C d e 1 4 6. Your answer should be a sequence of four integers, enter them separated by commas, for example: 14,2,23,-6
3. Let A be a 2 x 3 matrix, B a 3 × 4 matrix, and C a 4 x 5 matrix. The triple product ABC can be computed in two different ways: as (AB)C or as A(BC). (The fact that these always give the same answer is known as the associative law, Theorem 2(a) in section 2.1 of the textbook.) How many pairs of real numbers must be multiplied in the process of computing (AB)C? What about A(BC)? Which way of computing ABC is more efficient? To make sure you're on the right track in Problem 3, it takes eight multiplications to compute the product of two 2 x 2 matrices in the usual way. (If you're interested, you can read online about Strassen's algorithm which multiplies two 2x2 matrices in a more complicated way that uses only seven multiplications. Problem 3, however, asks only about “traditional" matrix multiplication using the row-column rule.)
Answer 11 and 12 using matrices
Which of the following matrix multiplications would be possible to do? Select one: a. a 5x6 matrix with a 6 x 3 matrix b. a 2 x 2 matrix with a 3 x3 matrix С. a 5x3 matrix with a 3 x 3 matrix d. a 4x3 matrix with a 3 x 3 matrix
Multiply matrix [1 2 3] by [5 o 4 2 1 03 0