Find the Uncoded 1 × 3 Row Matrices for the Message

Multiple Choice

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