Find the Uncoded 1 × 3 Row Matrices for the Message

question 257

Multiple Choice

Find the uncoded 1 × 3 row matrices for the message "TWO IF BY LAND" 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 $$\left[ \begin{array} { c c c } 0 & 3 & - 3 \\- 3 & - 3 & 3 \\- 3 & 3 & 0\end{array} \right]$$ .

• A)Uncoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } 20 & 23 & 15 \end{array} \right] \left[ \begin{array} { l l l } 0 & 9 & 6 \end{array} \right] \left[ \begin{array} { l l l } 0 & 2 & 25 \end{array} \right] \left[ \begin{array} { l l l } 0 & 12 & 1 \end{array} \right] } \\ \begin{array} { l l l l l l l l l l l l } T & \text { W } & \text { O } &&& \text { IF } &&&& \text { B Y } &&& \text { L A} \end{array} \\ { \left[ \begin{array} { l l l } 14 & 4 & 0 \end{array} \right] } \\ \mathrm { N } \mathrm { D } \\ \end{array}\] Encoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } - 114 & 36 & 9 \end{array} \right] \left[ \begin{array} { l l l } - 45 & - 9 & 27 \end{array} \right] \left[ \begin{array} { l l l } - 81 & 69 & 6 \end{array} \right] } \\ { \left[ \begin{array} { l l l } - 39 & - 33 & 36 \end{array} \right] \left[ \begin{array} { l l l } - 12 & 30 & - 30 \end{array} \right] } \end{array}\]
• B)Uncoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } 20 & 23 & 15 \end{array} \right] \left[ \begin{array} { l l l } 0 & 9 & 6 \end{array} \right] \left[ \begin{array} { l l l } 0 & 2 & 25 \end{array} \right] \left[ \begin{array} { l l l } 0 & 12 & 1 \end{array} \right] } \\ \begin{array} { l l l l l l l l l l l l } T & \text { W } & \text { O } &&& \text { IF } &&&& \text { B Y } &&& \text { L A} \end{array} \\ { \left[ \begin{array} { l l l } 14 & 4 & 0 \end{array} \right] } \\ \mathrm { N } \mathrm { D } \\ \end{array}\] Encoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } - 81 & 69 & 6 \end{array} \right] \left[ \begin{array} { l l l } - 39 & - 33 & 36 \end{array} \right] \left[ \begin{array} { l l l } - 12 & 30 & - 30 \end{array} \right] } \\ { \left[ \begin{array} { l l l l } - 114 & 36 & 9 \end{array} \right] \left[ \begin{array} { l l l } - 45 & - 9 & 27 \end{array} \right] } \end{array}\]
• C)Uncoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } 20 & 23 & 15 \end{array} \right] \left[ \begin{array} { l l l } 0 & 9 & 6 \end{array} \right] \left[ \begin{array} { l l l } 0 & 2 & 25 \end{array} \right] \left[ \begin{array} { l l l } 0 & 12 & 1 \end{array} \right] } \\ \begin{array} { l l l l l l l l l l l l } T & \text { W } & \text { O } &&& \text { IF } &&&& \text { B Y } &&& \text { L A} \end{array} \\ { \left[ \begin{array} { l l l } 14 & 4 & 0 \end{array} \right] } \\ \mathrm { N } \mathrm { D } \\ \end{array}\] Encoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } - 39 & - 33 & 36 \end{array} \right] \left[ \begin{array} { l l l } - 12 & 30 & - 30 \end{array} \right] \left[ \begin{array} { l l l l } - 114 & 36 & 9 \end{array} \right] } \\ { \left[ \begin{array} { l l l } - 45 & - 9 & 27 \end{array} \right] \left[ \begin{array} { l l l } - 81 & 69 & 6 \end{array} \right] } \end{array}\]
• D)Uncoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } 20 & 23 & 15 \end{array} \right] \left[ \begin{array} { l l l } 0 & 9 & 6 \end{array} \right] \left[ \begin{array} { l l l } 0 & 2 & 25 \end{array} \right] \left[ \begin{array} { l l l } 0 & 12 & 1 \end{array} \right] } \\ \begin{array} { l l l l l l l l l l l l } T & \text { W } & \text { O } &&& \text { IF } &&&& \text { B Y } &&& \text { L A} \end{array} \\ { \left[ \begin{array} { l l l } 14 & 4 & 0 \end{array} \right] } \\ \mathrm { N } \mathrm { D } \\ \end{array}\] Encoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } - 12 & 30 & - 30 \end{array} \right] \left[ \begin{array} { l l l l } - 114 & 36 & 9 \end{array} \right] \left[ \begin{array} { l l l } - 45 & - 9 & 27 \end{array} \right] } \\ { \left[ \begin{array} { l l l } - 81 & 69 & 6 \end{array} \right] \left[ \begin{array} { l l l l } - 39 & - 33 & 36 \end{array} \right] } \end{array}\]
• E)Uncoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } 20 & 23 & 15 \end{array} \right] \left[ \begin{array} { l l l } 0 & 9 & 6 \end{array} \right] \left[ \begin{array} { l l l } 0 & 2 & 25 \end{array} \right] \left[ \begin{array} { l l l } 0 & 12 & 1 \end{array} \right] } \\ \begin{array} { l l l l l l l l l l l l } T & \text { W } & \text { O } &&& \text { IF } &&&& \text { B Y } &&& \text { L A} \end{array} \\ { \left[ \begin{array} { l l l } 14 & 4 & 0 \end{array} \right] } \\ \mathrm { N } \mathrm { D } \\ \end{array}\] Encoded: \[\begin{array} { l } { \left[ \begin{array} { l l l } - 45 & - 9 & 27 \end{array} \right] \left[ \begin{array} { l l l } - 81 & 69 & 6 \end{array} \right] \left[ \begin{array} { l l l } - 39 & - 33 & 36 \end{array} \right] } \\ { \left[ \begin{array} { l l l } - 12 & 30 & - 30 \end{array} \right] \left[ \begin{array} { l l l } - 114 & 36 & 9 \end{array} \right] } \end{array}\]

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