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  = 0, A = 1, B = 2, and so...


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 takeA to be the 2 × 2 matrix
























34







21

.

 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 byA.

















Encrypted Matrix =





















34







21
































115201319914







2180919150

 =































1111760751338742







4484035573328

,



which we can also write as



[11  4  117  48  60  40  75  35  133  57  87  33  42  28].


To decipher the encoded message, multiply the encrypted matrix by


A−1.

 The following question uses the above matrixA for encoding and decoding.


Decode the following message, which was encrypted using the matrixA. (Include any appropriate spaces in your answer.)



[69  21  126  54  27  13  60  40  59  16  149  61  87  28]



Jun 04, 2022
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