Ask Your Teacher My Notes Question Part Points Submissions Used Matrices are

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Ask Your Teacher My Notes Question Part Points Submissions Used Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take < space > = 0, A = 1, B = 2, and so on. Thus, for example, "ABORT MISSION" becomes [1 2 15 18 20 0 13 9 19 19 9 15 14]. To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us take A to be the 2 × 2 matrix 3 1 2 4 . We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by A . Encrypted Matrix = 3 1 2 4
1 15 20 13 19 9 14 2 18 0 9 19 15 0 = 5 63 60 48 76 42 42 10 102 40 62 114 78 28 , which we can also write as [ 5 10 63 102 60 40 48 62 76 114 42 78 42 28 ]. To decipher the encoded message, multiply the encrypted matrix by A −1 . The following question uses the above matrix A for encoding and decoding. Decode the following message, which was encrypted using the matrix A . (Include any appropriate spaces in your answer.) [ 24 66 72 108 18 22 60 40 17 58 80 130 33 82 ] CORRECT ANSWER Home My Assignments WebAssign® 4.0 © 1997-2017 Advanced Instructional Systems, Inc. All rights reserved.
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