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 4 3 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 = 4 3 1 2 1 15 20 13 19 9 14 2 18 0 9 19 15 0 = 10 114 80 79 133 81 56 5 51 20 31 57 39 14 , which we can also write as [10 5 114 51 80 20 79 31 133 57 81 39 56 14]. to decipher the coded 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.) [57 33 126 54 29 11 80 20 46 29 145 65 74 41]