Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS" by assigning a number to each letter in the alphabet such as 1 = A, 2 = B, 3 = C and so on (with 0 assigned to a blank space);
Then encode the message using the encoding matrix

\left[ \begin{array} { c c c } 0 & - 2 & 1 \\- 1 & 1 & 1 \\1 & 2 & 0\end{array} \right]

.

A)Uncoded:

\begin{array} { l } { \left[ \begin{array} { l l l } 13 & 5 & 18\end{array} \right] \left[ \begin{array} { l l l } 18 & 25 & 0\end{array} \right] \left[ \begin{array} { l l l } 3 & 8 & 18\end{array} \right] \left[ \begin{array} { l l l } 9 & 19 & 20\end{array} \right] } \\\begin{array} { l l l l l l l l l l l l } M & \text { E } & \text { R } && \text { R Y } &&&&& \text { C R I } &&& \text { S T M}\end{array} \\{ \left[ \begin{array} { l l l } 13 & 1 & 19\end{array} \right] } \\\text { M A S } \\\end{array}

Encoded:

\begin{array} { l } { \left[ \begin{array} { l l l } 13 & 15 & 18\end{array} \right] \left[ \begin{array} { l l l } - 25 & - 11 & 43\end{array} \right] \left[ \begin{array} { l l l } 10 & 38 & 11\end{array} \right] } \\{ \left[ \begin{array} { l l l } 1 & 41 & 28\end{array} \right] \left[ \begin{array} { l l l } 18 & 13 & 14\end{array} \right] }\end{array}

B)Uncoded:

\begin{array} { l } { \left[ \begin{array} { l l l } 13 & 5 & 18\end{array} \right] \left[ \begin{array} { l l l } 18 & 25 & 0\end{array} \right] \left[ \begin{array} { l l l } 3 & 8 & 18\end{array} \right] \left[ \begin{array} { l l l } 9 & 19 & 20\end{array} \right] } \\\begin{array} { l l l l l l l l l l l l } M & \text { E } & \text { R } & \text { } & \text { R Y } &&&& \text { CR I } & & &\text { S } & \text { T }& \text { M }\end{array} \\{ \left[ \begin{array} { l l l } 13 & 1 & 19\end{array} \right] } \\\text { M A S } \\\end{array}

Encoded:

\begin{array} { l } { \left[ \begin{array} { l l l } 18 & 13 & 14\end{array} \right] \left[ \begin{array} { l l l } 13 & 15 & 18\end{array} \right] \left[ \begin{array} { l l l } - 25 & - 11 & 43\end{array} \right] } \\{ \left[ \begin{array} { l l l } 10 & 38 & 11\end{array} \right] \left[ \begin{array} { l c l } 1 & 41 & 28\end{array} \right] }\end{array}

C)Uncoded:

\begin{array} { l } { \left[ \begin{array} { l l l } 13 & 5 & 18\end{array} \right] \left[ \begin{array} { l l l } 18 & 25 & 0\end{array} \right] \left[ \begin{array} { l l l } 3 & 8 & 18\end{array} \right] \left[ \begin{array} { l l l } 9 & 19 & 20\end{array} \right] } \\\begin{array} { l l l l l l l l l l l l } M & \text { E } & \text { R }&&& \text {R Y } & &&\text { C R I } &&&& \text { S T M }\end{array} \\{ \left[ \begin{array} { l l l } 13 & 1 & 19\end{array} \right] } \\\text { M A S } \\\end{array}

Encoded:

\begin{array} { l } { \left[ \begin{array} { l l l } - 25 & - 11 & 43\end{array} \right] \left[ \begin{array} { l l l } 10 & 38 & 11\end{array} \right] \left[ \begin{array} { l l l } 1 & 41 & 28\end{array} \right] } \\{ \left[ \begin{array} { l l l } 18 & 13 & 14\end{array} \right] \left[ \begin{array} { l l l } 13 & 15 & 18\end{array} \right] }\end{array}

D)Uncoded:

\begin{array} { l } { \left[ \begin{array} { l l l } 13 & 5 & 18\end{array} \right] \left[ \begin{array} { l l l } 18 & 25 & 0\end{array} \right] \left[ \begin{array} { l l l } 3 & 8 & 18\end{array} \right] \left[ \begin{array} { l l l } 9 & 19 & 20\end{array} \right] } \\\begin{array} { l l l l l l l l l l l l } M & \text { E } & \text { R } &&\text { R Y } &&&& \text { C R I } &&&& \text { S T M}\end{array} \\{ \left[ \begin{array} { l l l } 13 & 1 & 19\end{array} \right] } \\\text { M A S } \\\end{array}

Encoded:

\begin{array} { l } { \left[ \begin{array} { l l l } 10 & 38 & 11\end{array} \right] \left[ \begin{array} { l l l } 1 & 41 & 28\end{array} \right] \left[ \begin{array} { l l l } 18 & 13 & 14\end{array} \right] } \\{ \left[ \begin{array} { l l l } 13 & 15 & 18\end{array} \right] \left[ \begin{array} { l l l } - 25 & - 11 & 43\end{array} \right] }\end{array}

E)Uncoded:

\begin{array} { l } { \left[ \begin{array} { l l l } 13 & 5 & 18\end{array} \right] \left[ \begin{array} { l l l } 18 & 25 & 0\end{array} \right] \left[ \begin{array} { l l l } 3 & 8 & 18\end{array} \right] \left[ \begin{array} { l l l } 9 & 19 & 20\end{array} \right] } \\\begin{array} { l l l l l l l l l l l l } M & \text { E } & \text { R } &&\text { R Y } &&&& \text { C R I } &&&& \text { S T M}\end{array} \\{ \left[ \begin{array} { l l l } 13 & 1 & 19\end{array} \right] } \\\text { M A S } \\\end{array}

Encoded:

\begin{array} { l } { \left[ \begin{array} { l l l } 1 & 41 & 28\end{array} \right] \left[ \begin{array} { l l l } 18 & 13 & 14\end{array} \right] \left[ \begin{array} { l l l } 13 & 15 & 18\end{array} \right] } \\{ \left[ \begin{array} { l l l } - 25 & - 11 & 43\end{array} \right] \left[ \begin{array} { l l l } 10 & 38 & 11\end{array} \right] } \\\end{array}

Find X and Y A)x = -2, Y = 10 B)x = 2, Y

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Find X and Y A)x = -2, Y = 10
B)x = 2, Y

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