Question 8.4.6: Encoding a Word Use matrices to encode the word MATH

Step 1 Express the word numerically. As shown previously, the numerical equivalent of MATH is 13, 1, 20, 8.

Step 2 List the numbers in step 1 by columns and form a square matrix. The 2 × 2 matrix for the numerical equivalent of MATH, 13, 1, 20, 8, is

\left[\begin{array}{rr}13 & 20 \\1 & 8\end{array}\right].

Step 3 Multiply the matrix in step 2 by a square invertible matrix. We will use \left[\begin{array}{rr}-2 & -3 \\ 3 & 4\end{array}\right] as the coding matrix.

Step 4 Use the numbers, by columns, from the coded matrix in step 3 to write the encoded message. The encoded message is -29, 43, -64, 92.