1. Using Inverse Matrices in Real Life
4.4 Cont.

2. Cryptograms A message written according to a secret code.
From the Greek word Kryptos meaning hidden and gramma meaning letter

3. Steps to create a cryptogram
Assign a number to each letter in the alphabet with out a blank space.
Convert the message to numbers partitioned into 1x2 uncoded row matrices.
To encode a message, choose a 2x2 matrix A that has an inverse and multiply the uncoded row matrices by A on the right to obtain coded row matrices

4. Convert: GET HELP 7 5 20 0 8 5 12 16 [7 5 ][20 0][8 5][12 16]
Encode use A=

5. Encoding Cont…
The coded message is: 9,11,40,60,11,14,8,4

6. Decoding using Matrices
If you don’t know the matrix used to incode - decoding would be very difficult. When a larger coding matrix is used, decoding is even more difficult. But for an authorized receiver who knows the matrix A, decoding is simple.
The receiver only needs to multiply the coded row matrices by A-1 on the right to retrieve the uncoded message.

7. Decoding using Matrices cont…
Use to decode:
-4,3,-23,12,-26,13,15,-5,31,-5,-38,19, ,12,20,0,75,-25
First, group the numbers in twos.
Find the inverse of the matrix used to code.
Then multiply the 1x2 coded martices by the inverse on the right to get the decoded numbers.

9. The decoded numbers are:
2,5,1,13,0,13,5,0,21,16,0,19,3,15,20,20,25,0
Now use the coded alphabet to translate to:
BEAM_ME_UP_SCOTTY_