Encode and Decode Messages
-Use the coding matrix $A = \left[ \begin{array} { r r } - 1 & - 3 \ 2 & 5 \end{array} \right]$ to encode the message CARE.
A) $\left[ \begin{array} { r r } - 6 & - 33 \ 11 & 61 \end{array} \right]$
B) $\left[ \begin{array} { r r } - 57 & - 16 \ 96 & 27 \end{array} \right]$
C) $\left[ \begin{array} { l l } 18 & 105 \ - 7 & - 4 \end{array} \right]$
D) $\left[ \begin{array} { l r } - 1 & - 8 \ - 4 & - 29 \end{array} \right]$

Question

Quizplus · Accepted Answer

To encode the message "CARE" using the matrix $A$, we first convert the letters to numbers based on their position in the alphabet: C=3, A=1, R=18, E=5. We then group these into 2x1 matrices (or vectors) and multiply each by the coding matrix $A$. For "CA" and "RE", we have:$$A \times \left[ \begin{array} { r } 3 \ 1 \end{array} \right] = \left[ \begin{array} { r r } - 1 & - 3 \ 2 & 5 \end{array} \right] \times \left[ \begin{array} { r } 3 \ 1 \end{array} \right] = \left[ \begin{array} { r } - 6 \ 11 \end{array} \right]$$$$A \times \left[ \begin{array} { r } 18 \ 5 \end{array} \right] = \left[ \begin{array} { r r } - 1 & - 3 \ 2 & 5 \end{array} \right] \times \left[ \begin{array} { r } 18 \ 5 \end{array} \right] = \left[ \begin{array} { r } - 33 \ 61 \end{array} \right]$$Combining these results gives the encoded matrix $\left[ \begin{array} { r r } - 6 & - 33 \ 11 & 61 \end{array} \right]$, which matches option A.

Encode and Decode Messages -Use the Coding Matrix A=[−1−325]A = \left[ \begin{array} { r r } - 1 & - 3 \\ 2 & 5 \end{array} \right]A=[−12​−35​]

Encode and Decode Messages
-Use the Coding Matrix $A = \left[ \begin{array} { r r } - 1 & - 3 \\ 2 & 5 \end{array} \right]$