Cryptography. Matrices can be used to encode and decode secret messages. Suppose we have a simple cipher where each letter of the alphabet is simply replaced by its position in the English alphabet (and 0 denotes a space):
space a b c d e f g h i j k l m
0 1 2 3 4 5 6 7 8 9 10 11 12 13
n o p q r s t u v w x y z
14 15 16 17 18 19 20 21 22 23 24 25 26
For example, "mathisfun" would become the sequence "13 1 20 8 9 19 6 21 14." If we put it in a 3 x 3 matrix, one possibility is A = (13 1 20 / 8 9 19 / 6 21 14).
Next, in order to encode the message, we multiply A on the left (= CA) by the following matrix: C = (0 -2 1 / -4 5 -2 / 5 -3 1)
In order to decode, we need to multiply on the left by another matrix M. You then get back your original message A (that is, MCA = A).
a) Figure out what matrix to use for M and compute it.
b) Use it to decode the following matrix: B = (8 -25 2 / -43 -2 -24 / 42 45 27)
That is, do the following matrix multiplication: MB. What is the message in English?