Matrices are commonly used to encrypt data. Here is a simple form such an encryption can...

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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 on. Thus, for example, "ABORT MISSION" becomes [12 15 18 20 0 13 9 19 19 9 15 14]. 1 2 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 x2 matrix place if we have an odd number of characters) and then multiply on the left by A. [43] We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last 1 2 Encrypted Matrix = 4 3 ][ 1 15 20 13 19 9 14 2 18 0 9 19 15 0 5 51 20 31 57 39 14 10 114 80 79 133 81 56 which we can also write as [5 10 51 114 20 80 31 79 57 133 39 81 14 56]. 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.) [33 57 54 126 11 29 20 80 29 46 65 145 41 74] 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 on. Thus, for example, "ABORT MISSION" becomes [12 15 18 20 0 13 9 19 19 9 15 14]. 1 2 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 x2 matrix place if we have an odd number of characters) and then multiply on the left by A. [43] We can first arrange the coded sequence of numbers in the form of a matrix with two rows (using zero in the last 1 2 Encrypted Matrix = 4 3 ][ 1 15 20 13 19 9 14 2 18 0 9 19 15 0 5 51 20 31 57 39 14 10 114 80 79 133 81 56 which we can also write as [5 10 51 114 20 80 31 79 57 133 39 81 14 56]. 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.) [33 57 54 126 11 29 20 80 29 46 65 145 41 74]