Question

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 x 2 matrix [3 4; 1 2]. 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 4; 1 2] [1 15 20 13 19 9 14; 2 18 0 9 19 15 0] = [11 117 60 75 133 87 42; 5 51 20 31 57 39 14], which we can also write as [11 5 117 51 60 20 75 31 133 57 87 39 42 14]. 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.) [69 33 126 54 27 11 60 20 59 29 149 65 87 41]

          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 x 2 matrix [3 4; 1 2]. 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 4; 1 2] [1 15 20 13 19 9 14; 2 18 0 9 19 15 0]
= [11 117 60 75 133 87 42; 5 51 20 31 57 39 14],
which we can also write as
[11 5 117 51 60 20 75 31 133 57 87 39 42 14].
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.)
[69 33 126 54 27 11 60 20 59 29 149 65 87 41]

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 x 2 matrix [3 4; 1 2]. 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 4; 1 2] [1 15 20 13 19 9 14; 2 18 0 9 19 15 0]
= [11 117 60 75 133 87 42; 5 51 20 31 57 39 14],
which we can also write as
[11 5 117 51 60 20 75 31 133 57 87 39 42 14].
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.)
[69 33 126 54 27 11 60 20 59 29 149 65 87 41]

Added by Catherine V.

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