Encode the message “ I LOVE LINEAR ALGEBRA” using the technique described in
. Verify that the coded message decodes correctly.
Consider the matrix
Add the first row to both the second and third rows to obtain
Now add the second row to the third
Finally, add rows two and three together, multiply the sum by
and add to the first row. We obtain the matrix
Verify that det
This must be the case since the original upper triangular matrix has determinant
and we only added multiples of one row to another. The inverse of
is
Now consider the message
TODAY IS A GOOD DAY
To every letter we will associate a number. An easy way to do that is to associate 0 to a space,
to
etc. Another way is to associate
to a blank or space,
to
to
to
to
etc. Let us use the second choice. We encode our message as follows:
Now we rearrange these numbers into a matrix B. For example, sequence the numbers by columns, adding zeros in the last column if necessary. The matrix B must have three rows for the product AB to be defined.
Now perform the product AB. We get
The encrypted message to be sent is
26.