Chapter 8, Problem 20PS

(a)

To determine

To write and solve two system of equations in order to find the value of and

Answer to Problem 20PS

The decoding matrix is-

  

Explanation of Solution

Given Information:

The following cryptogram is given:

  

Consider the following cryptogram

  

So, the coded message is-

  

The decoding matrix is:

  

It is also given that

  

Now, it is given that-

  

So, the system of linear equations are as follows-

  

And

  

Now, the augmented matrix for both the equations are:

  

Applying the Gauss Jordan elimination and applying row transformations:

  

So, the values are −

  

So, the decoding matrix is −

  

b.

To determine

To decode the message.

Answer to Problem 20PS

The message is -

JOHN RETURN TO BASE

Explanation of Solution

Now, the message can be decoded by multiplying the decoding matrix with the coded matrix as follows-

  

Therefore, the un-coded matrices are:

  

So, the message in cryptography can be written as

  

Hence, the original message is JOHN RETURN TO BASE.