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Math Project - Sheet1

The document provides instructions for encoding and decoding a message using matrix multiplication and transformations. It encodes the message "♡We are cute & smart. :)" by transforming the letters to numbers, multiplying them by a matrix, transforming the results back to letters. It then decodes the encoded message by multiplying the encoded numbers by the inverse matrix and transforming back to the original message. The encoding and decoding is demonstrated in 3 steps with matrices in each step.

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118 views2 pages

Math Project - Sheet1

The document provides instructions for encoding and decoding a message using matrix multiplication and transformations. It encodes the message "♡We are cute & smart. :)" by transforming the letters to numbers, multiplying them by a matrix, transforming the results back to letters. It then decodes the encoded message by multiplying the encoded numbers by the inverse matrix and transforming back to the original message. The encoding and decoding is demonstrated in 3 steps with matrices in each step.

Uploaded by

api-327817913
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Coding Chart

ENCODING MESSAGE

Message to encode: We are cute & smart. :)


E U S R
W A T & & M T :
E R C E A . )

Transform the matrices to their numerical equivalents :


0 30 8 24 30 22 21 30
26 4 30 23 & 31 16 23 2
8 21 6 8 30 4 1 3

Matrix C
3 -2 2
-1 1 -1
1 0 1

Multiply the matrices by Matrix C :


-36 124 -24 42 88 42 19 92
18 -47 16 -9 & -29 -10 1 -31
8 51 14 32 60 26 22 33

Reduce the numbers to equivalent Mod 32 :


28 28 8 10 24 10 19 28
18 17 16 23 & 3 22 1 1
8 19 14 0 28 26 22 1

Transform the matrices to their equivalent letters :


Y Y E G U G P Y
O N M T & ) S . .
E P K Y W S .
The encoded message is: YOEYNPEMKGTU)YGSWP.SY..
DECODING MESSAGE

Transform the matrices to their numerical equivalents


28 28 8 10 24 10 19 28
18 17 16 23 & 3 22 1 1
8 19 14 0 28 26 22 1

Inverse of Matrix C
1 2 0
0 1 1
-1 -2 1

Multiply the matrices by inverse of Matrix C :


64 62 40 56 30 54 21 30
26 36 30 23 & 31 48 23 2
-56 -43 -26 -56 -2 -28 1 -29

Reduce the numbers to equivalent Mod 32 :


0 30 8 24 30 22 21 30
26 4 30 23 & 31 16 23 2
8 21 6 8 30 4 1 3

The decoded message is: We are cute & smart. :)

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