Question #2015504: Applications of Linear Algebra


Question: Secret messages can be encoded by using a code and an encoding matrix. Suppose we have the following code:

We encode an empty space by 0. Let the encoding matrix be

\[E=\left[ \begin{matrix}
1 & -2 \\
-2 & 3 \\
\end{matrix} \right]\]

Then we can encode a message by taking every two letters of the message, converting them to their corresponding numbers, creating a 2 × 1 matrix, and then multiplying each matrix by E.

(a) Use this matrix to encode the message “Happy new year”

(b) Use this code and matrix to decode

\[\left[ \begin{matrix}
13 \\
-31 \\
\end{matrix} \right],\left[ \begin{matrix}
6 \\
-15 \\
\end{matrix} \right],\left[ \begin{matrix}
-11 \\
9 \\
\end{matrix} \right],\left[ \begin{matrix}
5 \\
-10 \\
\end{matrix} \right],\left[ \begin{matrix}
0 \\
-1 \\
\end{matrix} \right],\left[ \begin{matrix}
-19 \\
27 \\
\end{matrix} \right]\]

Solution: The solution consists of 362 words (4 pages)
Deliverables: Word Document

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