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

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 [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 . 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 = 1 2 1 15 20 13 19 9 14 3 4 2 18 0 9 19 15 0 5 51 20 31 57 39 14 11 117 60 75 133 87 42 which we can also write as [5 11 51 117 20 60 31 75 57 133 39 87 14 42]. To decipher the encoded message, multiply the encrypted matrix by A". 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 69 54 126 11 27 20 60 29 59 65 149 41 87]