Chapter 8, Problem 122RE

To determine

To decode the cryptogram using inverse of the matrix.

Answer to Problem 122RE

The decoded message is “MAY THE FORCE BE WITH YOU”.

Explanation of Solution

Given Information:

The following cryptogram is given:

  

Consider the following matrix,

  

And cryptogram is as listed below,

  

First find

Step 1: Write the matrix A on the left side and the identity matrix I on the right to obtain

  

Step 2: Reduce A to I using elementary row operations on entire matrixto obtain

Perform row operations as follows:

  

Perform

  

Perform

  

Perform

  

Perform

  

Perform

  

Perform

  

Perform

  

So, the matrix A is invertible and its inverse is,

  

Make group of three to form coded matrices. Multiply each coded row matrix by That is,

  

1.

  

2.

  

3.

  

4.

  

5.

  

6.

  

7.

  

8.

  

9.

  

So decoded message is,

“13 1 25 0 20 8 5 0 6 15 18 3 5 0 2 5 0 23 9 20 8 0 25 15 21 0 0”

Write alphabets for number and blank space for zero.

Hence message is “MAY THE FORCE BE WITH YOU”