Using Inverse Matrices in Real Life

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# Using Inverse Matrices in Real Life - PowerPoint PPT Presentation

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.

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### 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_