1(b). Cryptography is concerned with keeping communications private. Today govemments usesophisticated methods of coding and decoding messages. One type of code, which isextremely difficult to break, makes use ofa large matrix to encode a message. The receiverof the message decodes it using the inverse of the matrix. This first matrix is called theencoding matrix and its inverse is called the decoding matrix. If the following matrixwritten is an encoding matrix of a govemment agency's sophisticated method of encodingoutgoing messages,-2-21.4Find the Inverse of the above message matrix which will represent the decoding matrix.

Inverse of the matrix is 2394 -347 1394 547 1347 1147 994 747 194

Answered: -2 5 -2 1 4 1 4 -7) Find the Inverse of…

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-2 5 -2 1 4 1 4 -7) Find the Inverse of the above message matrix which will represent the decoding matrix.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Matrices And Determinants

Section: Chapter Questions

Problem 14T

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(2) Cryptography is the process of coding and decoding messages. One type of code that is extremely difficult to break involves using a large invertible matrix to encode a message. The receiver of the message decodes it using the inverse of the matrix. The first matrix is called the encoding matrix and its inverse is called the decoding matrix. The following example uses a 2 × 2 to illustrate the method. First we start by identifying the symbols A, B, C,..., Z with the numbers 1, ..., 26. Let a space between the words be denoted by the number 27. For example, the message "HELLO ." will be coded as 8 5 12 12 15. The basic idea is to write the message as a matrix. For example, we may write "HELLO" as the 2 × 3 matrix 8 12 15 M = 5 12 27 If we now take a 2 × 2 invertible matrix A, we may encrypt the message as AM. For example, if 3 2 A = 2) the message "HELLO." becomes "34 45, 60 72, 99 102". This message can be decoded by reversing the encoding process. PROBLEM TO BE TURNED IN: Use the…
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