Find the Uncoded 1 × 3 Row Matrices for the Message

question 268

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

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Definitions:

Market Price

The current price at which an asset or service can be bought or sold in a marketplace.

Return on Total Assets

A financial ratio that measures the profitability of a company in relation to its total assets, indicating how efficient management is at using its assets to generate earnings.

Interest Expense

A financial charge for borrowing money or the cost incurred on debt.

Net Income

The total profit of a company after all expenses and taxes have been subtracted from total revenue.