Chapter 4.5, Problem 88E

Problems $85\text{-}88$ require the use of a graphing calculator or a computer. Use the $5\times 5$ encoding matrix $C$ given below. Form a matrix with $5$ rows and as many columns as necessary to accommodate the message.

$C=\left[\begin{array}{ccccc}1& 0& 1& 0& 1\\ 0& 1& 1& 0& 3\\ 2& 1& 1& 1& 1\\ 0& 0& 1& 0& 2\\ 1& 1& 1& 2& 1\end{array}\right]$

Cryptography. The following message was encoded with matrix $C$. Decode this message:

$\begin{array}{l}\text{25 75 55 35 50 43 83 54 60 53 25 13}\\ \text{59 9 53 15 35 40 15 45 33 60 60 36}\\ \text{51 15 7 37 0 22}\end{array}$