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Math Project

The document discusses encoding and decoding a message using a matrix. It first defines an encoding matrix and uses it to encode the message "junior_year._I_somehow_have_mixed_emotions" into numbers. It then decodes the encoded message back into text. The encoding and decoding process is demonstrated through performing operations on the encoding matrix.

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110 views8 pages

Math Project

The document discusses encoding and decoding a message using a matrix. It first defines an encoding matrix and uses it to encode the message "junior_year._I_somehow_have_mixed_emotions" into numbers. It then decodes the encoded message back into text. The encoding and decoding process is demonstrated through performing operations on the encoding matrix.

Uploaded by

api-462603552
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Message: junior_year.

_I_somehow_have_mixed_emotio

Encoding matrix:

[ ]

det = Reduce to row echelon form =

[ ] [ ]

det = diagonal product of the matrix = -1

[ ]

Interchanging two rows negate the determinant, therefore multiply the result by ( ) ( )

=1

_=0 F=6 L = 12 R = 18 X = 24  = 30

A=1 G=7 M = 13 S = 19 Y = 25 ) = 31

B=2 H=8 N = 14 T = 20 Z = 26 1 = 32

C=3 I=9 O = 15 U = 21 . = 27 9 = 33

D=4 J = 10 P = 16 V = 22 ; = 28 2 = 34

E=5 K = 11 Q = 17 W = 23 : = 29

j u n i o r _ y e a r . _ I _ s o m e h

10 21 14 9 15 18 0 25 5 1 18 27 0 9 0 19 15 13 5 8

o w _ h a v e _ m i x e d _ e m o t i o

15 23 0 8 1 22 5 0 13 9 24 5 4 0 5 13 15 20 9 15
Encoding:

[ ] [ ] [ ]

A11 = (-1) x 10 + 6 x 15 + 2 x 5 + 4 x 0 + 7 x 15 = 196

A12 = (-1) x 21 + 6 x 18 + 2 x 1 + 4 x 9 + 7 x 13 = 216

A13 = (-1) x 14 + 6 x 0 + 2 x 18 + 4 x 0 + 7 x 5 = 57

A14 = (-1) x 9 + 6 x 25 + 2 x 27 + 4 x 19 + 7 x 8 = 327

A21 = 0 x 10 + 1 x 15 + 8 x 5 + 9 x 0 + 3 x 15 = 100

A22 = 0 x 21 + 1 x 18 + 8 x 1 + 9 x 9 + 3 x 13 = 146

A23 = 0 x 14 + 1 x 0 + 8 x 18 + 9 x 0 + 3 x 5 = 159

A24 = 0 x 9 + 1 x 25 + 8 x 27 + 9 x 19 + 3 x 8 = 436

A31 = 0 x 10 + 0 x 15 + 3 x 5 + 2 x 0 + 5 x 15 = 90

A32 = 0 x 21 + 0 x 18 + 3 x 1 + 2 x 9 + 5 x 13 = 86

A33 = 0 x 14 + 0 x 0 + 3 x 18 + 2 x 0 + 5 x 5 = 79

A34 = 0 x 9 + 0 x 25 + 3 x 27 + 2 x 19 + 5 x 8 = 159

A41 = 0 x 10 + 0 x 15 + 5 x 5 + 3 x 0 + (-6) x 15 = -65

A42 = 0 x 21 + 0 x 18 + 5 x 1 + 3 x 9 + (-6) x 13 = -46

A43 = 0 x 14 + 0 x 0 + 5 x 18 + 3 x 0 + (-6) x 5 = 60

A44 = 0 x 9 + 0 x 25 + 5 x27 + 3 x 19 + (-6) x 8 = 144

A51 = 0 x 10 + 0 x 15 + 0 x 5 + 0 x 0 + 1 x 15 = 15

A52 = 0 x 21 + 0 x 18 + 0 x 1 + 0 x 9 + 1 x 13 = 13

A53 = 0 x 14 + 0 x 0 + 0 x 18 + 0 x 0 + 1 x 5 = 5

A54 = 0 x 9 + 0 x 25 + 0 x 27 + 0 x 19 + 1 x 8 = 8

Encrypted message:

[ ]
=

[ ] [ ] [ ]

A11 = (-1) x 15 + 6 x 1 + 2 x 13 + 4 x 4 + 7 x 15 = 138

A12 = (-1) x 23 + 6 x 22 + 2 x 9 + 4 x 0 + 7 x 20 = 267

A13 = (-1) x 0 + 6 x 5 + 2 x 24 + 4 x 5 + 7 x 9 = 161

A14 = (-1) x 8 + 6 x 0 + 2 x 5 + 4 x 13 + 7 x 15 = 159

A21 = 0 x 15 + 1 x 1 + 8 x 13 + 9 x 4 + 3 x 15 = 186

A22 = 0 x 23 + 1 x22 + 8 x 9 + 9 x 0 + 3 x 20 = 154

A23 = 0 x 0 + 1 x 5 + 8 x 24 + 9 x 5 + 3 x 9 = 269

A24 = 0 x 8 + 1 x 0 + 8 x 5 + 9 x 13 + 3 x 15 = 202

A31 = 0 x 15 + 0 x 1 + 3 x 13 + 2 x 4 + 5 x 15 = 122

A32 = 0 x 23 + 0 x 22 + 3 x 9 + 2 x 0 + 5 x 20 = 127

A33 = 0 x 0 + 0 x 5 + 3 x 24 + 2 x 5 + 5 x 9 = 127

A34 = 0 x 8 + 0 x 0 + 3 x 5 + 2 x 13 + 5 x 15 = 116

A41 = 0 x 15 + 0 x 1 + 5 x 13 + 3 x 4 + (-6) x 15 = -13

A42 = 0 x 23 + 0 x 22 + 5 x 9 + 3 x 0 + (-6) x 20 = -75

A43 = 0 x 0 + 0 x 5 + 5 x 24 + 3 x 5 + (-6) x 9 = 81

A44 = 0 x 8 + 0 x 0 + 5 x 5 + 3 x 13 + (-6) x 15 = -26

A51 = 0 x 15 + 0 x 1 + 0 x 13 + 0 x 4 + 1 x 15 = 15

A52 = 0 x 15 + 0 x 1 + 0 x 13 + 0 x 0 + 1 x 20 = 20

A53 = 0 x 15 + 0 x 1 + 0 x 13 + 0 x 0 + 1 x 20 = 9

A54 = 0 x 15 + 0 x 1 + 0 x 13 + 0 x 0 + 1 x 20 = 15

Encrypted message:

[ ]
Decoding:

[ ] [ ] [ ]

A11 = (-1) x 196 + 6 x 100 + (-112) x 90 + 58 x (-65) + 897 x 15 = 10

A12 = (-1) x 216 + 6 x 146 + (-112) x 86 + 58 x (-46) + 897 x 13 = 21

A13 = (-1) x 57 + 6 x 159 + (-112) x 79 + 58 x 60 + 897 x 5 = 14

A14 = (-1) x 327 + 6 x 436 + (-112) x 159 + 58 x 144 + 897 x 8 = 9

A21 = 0 x 196 + 1 x 100 + (-21) x 90 + 11 x (-65) + 168 x 15 = 15

A22 = 0 x 216 + 1 x 146 + (-21) x 86 + 11 x (-46) + 168 x 13 = 18

A23 = 0 x 57 + 1 x 159 + (-21) x 79 + 11 x 60 + 168 x 5 = 0

A24 = 0 x 327 + 1 x 436 + (-21) x 159 + 11 x 144 + 168 x 8 = 25

A31 = 0 x 196 + 0 x 100 + (-3) x 90 + 2 x (-65) + 27 x 15 = 5

A32 = 0 x 216 + 0 x 146 + (-3) x 86 + 2 x (-46) + 27 x 13 = 1

A33 = 0 x 57 + 0 x 159 + (-3) x 79 + 2 x 60 + 27 x 5 = 18

A34 = 0 x 327 + 0 x 436 + (-3) x 159 + 2 x 144 + 27 x 8 = 27

A41 = 0 x 196 + 0 x 100 + 5 x 90 + (-3) x (-65) + (-43) x 15 = 15

A42 = 0 x 216 + 0 x 146 + 5 x 86 + (-3) x (-46) + (-43) x 13 = 13

A43 = 0 x 57 + 0 x 159 + 5 x 79 + (-3) x 60 + (-43) x 5 = 5

A44 = 0 x 327 + 0 x 436 + 5 x 159 + (-3) x 144 + (-43) x 8 = 8

Decoded message:

[ ]
=

[ ][ ] [ ]

A11 = (-1) x 138 + 6 x 186 + (-112) x 122 + 58 x (-13) + 897 x 15 = 15

A12 = (-1) x 267+ 6 x 154 + (-112) x 127 + 58 x (-75) + 897 x 20 = 23

A13 = (-1) x 161 + 6 x 269 + (-112) x 127 + 58 x 81 + 897 x 9 = 0

A14 = (-1) x 159 + 6 x 202 + (-112) x 116 + 58 x (-26) + 897 x 15 = 8

A21 = 0 x 138 + 1 x 186 + (-21) x 122 + 11 x (-13) + 168 x 15 = 1

A22 = 0 x 267 + 1 x 154 + (-21) x 127 + 11 x (-75) + 168 x 20 = 22

A23 = 0 x 161 + 1 x 269 + (-21) x 127 + 11 x 81 + 168 x 9 = 5

A24 = 0 x 159 + 1 x 202 + (-21) x 116 + 11 x (-26) + 168 x 15 = 0

A31 = 0 x 138 + 0 x 186 + (-3) x 122 + 2 x (-13) + 27 x 15 = 13

A32 = 0 x 267 + 0 x 154 + (-3) x 127 + 2 x (-75) + 27 x 20 = 9

A33 = 0 x 161 + 0 x 269 + (-3) x 127 + 2 x 81 + 27 x 9 = 24

A34 = 0 x 159 + 0 x 202 + (-3) x 116 + 2 x (-26) + 27 x 15 = 5

A41 = 0 x 138 + 0 x 186 + 0 x 122 + 0 x (-13) + 1 x 15 = 15

A42 = 0 x 267 + 0 x 154 + 0 x 127 + 0 x (-75) + 1 x 20 = 20

A43 = 0 x 161 + 0 x 269 + 0 x 127 + 0 x 81 + 1 x 9 = 9

A44 = 0 x 159 + 0 x 202 + 0 x 116 + 0 x (-26) + 1 x 15 = 15

Decoded message:

[ ]
Inverse:

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-( ) :

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