Using Inverse Matrices in Real Life

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Using Inverse Matrices in Real Life

• 4.4 Cont.

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Cryptograms

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

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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

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Convert GET HELP

• 7 5 20 0 8 5 12 16
• 7 5 20 08 512 16
• Encode use A

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

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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.

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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_

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Assignment