Using Inverse Matrices in

Real Life

4.4 Cont.

Cryptograms

A message written according to a secret code.

From the Greek word Kryptos meaning hidden and gramma meaning letter

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

Convert: GET HELP 7 5 20 0 8 5 12 16

[7 5 ][20 0][8 5][12 16]

Encode use A=

21

32

Encoding Cont… 1191021514

21

3257

604021

32020

1411102451621

3258

483236162421

321612

The coded message is: 9,11,40,60,11,14,8,4

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.

Decoding using Matrices cont… Use to decode:

-4,3,-23,12,-26,13,15,-5,31,-5,-38,19, -21,12,20,0,75,-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.

12

13A

32

11

32

11

23

11A

5232

1134

13132

111223

13032

111326

0532

11515

162132

11531

19032

111938

15332

111221

202032

11020

02532

112575

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_