Encoding and Decoding Information
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Use the table for swapping letters with numbers and the matrix \(C = \left[ {\begin{array}{*{20}{c}}1&2\\2&1\end{array}} \right]\) to encode the message \(\left[ {\begin{array}{*{20}{c}}C&A&N\\A&P&E\end{array}} \right]\)
\begin{array}{|c|c|c|c|c|}
\hline \text { A } & \text { C } & \text { E } & \text { N } & \text { P } \\
\hline 1 & 3 & 5 & 14 & 16 \\
\hline
\end{array}
\begin{aligned}
B=&\left[\begin{array}{ll}
C A N \\
A P E
\end{array}\right]=\left[\begin{array}{ccc}
3 & 1 & 14 \\
1 & 16 & 5
\end{array}\right] \\
CB &=\left[\begin{array}{ll}
1 & 2 \\
2 & 1
\end{array}\right]\left[\begin{array}{lll}
3 & 1 & 14 \\
1 & 16 & 5
\end{array}\right] \\
&=\left[\begin{array}{lll}
5 & 33 & 24 \\
7 & 18 & 33
\end{array}\right]
\end{aligned}
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