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Using Inverse Matrices in Real Life

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From the Greek word Kryptos meaning hidden and gramma meaning letter ... Assign a number to each letter in the alphabet with out a blank space. ... – PowerPoint PPT presentation

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Title: Using Inverse Matrices in Real Life


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 08 512 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 dont 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,
    -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.

8
(No Transcript)
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_

10
Assignment
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