Using Inverse Matrices in Real Life

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=

Encoding Cont… 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.

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_

Assignment

Using Inverse Matrices in Real Life