Matrix Algebra to decode a message

[blueparukia]

Homework Statement

Hey, I need to decode a message hidden in a Matrix as a practice activity, and I'm rather stuck.

The alphabet key is starting from the letter A,numbered using first:
a)Fibonacci Sequence
b)Prime Numbers
c)Counting Numbers
d)No numbers higher than 27

http://latex.sidoh.org/?render64=WD1cWyBcbGVmdCggXGJlZ2lue2FycmF5fXtjY2N9DQoxICYgMCAmIDEgXFwNCjAgJiAxICYgMCBcXA0KMSAmIDAgJiAxIFxlbmR7YXJyYXl9IFxyaWdodClcXQ==
http://latex.sidoh.org/?render64=WT1cWyBcbGVmdCggXGJlZ2lue2FycmF5fXtjY2N9DQotMiAmIDIgJiAxIFxcDQowICYgMiAmIDQgXFwNCi0yICYgNCAmIDQgXGVuZHthcnJheX0gXHJpZ2h0KVxd
http://latex.sidoh.org/?render64=VT1cWyBcbGVmdCggXGJlZ2lue2FycmF5fXtjY2N9DQo0MiAmIDEyMSAmIDEzMSBcXA0KMjUgJiA5MyAmIDkyIFxcDQoyNyAmIDk3ICYgOTcgXFwNCjI5ICYgMTExICYgMTEyIFxcDQo3ICYgMzYgJiAzMiBcXA0KMzQgJiA4OCAmIDk4IFxlbmR7YXJyYXl9IFxyaWdodClcXQ==
Now we have the hard part, we have to use "matrix algebra" (which we learned over a month ago) to find the real message. An instinct tells me I have to either find an inverse or identity, but I don't know how to do that with a matrix.

Homework Equations

The encoded matrix, U, is the product of (X+Y)^T

The Attempt at a Solution

Not a whole heap since I only have a sheet and now textbooks, but still I did the alphabet key:

First we have to solve the alphabet key, which I've done:
A=1
B=2
C=3
D=5
E=8
F=13 
G=21
H=7
I=11
J=17
K=19
L=23
M=4
N=6
O=9
P=10
Q=12
R=14
S=15
T=16
U=18
V=20
W=22
X=24
Y=25
Z=26
Space=27

And I know I have to times something by an inverse or identity, but I don't know what. THe only thing I can remember on Matrix algebra is AX=something.








I know this is not the greatest attempt, but I've worked 17 hours this weekend, I have no idea what to do, and after this I still have to work out how to reencode a message (which I should hopefully be able to work out)

 

[Nino MMP]

so any help would be great. The first step is to find the inverse or identity matrix for the given matrix. To do this, you can use a program like MATLAB or Wolfram Alpha. Once you have the inverse or identity matrix, you can then multiply the given matrix by it to get the original message.

 

[Architeuthis Dux]

Dear student,

It seems that you are on the right track with using matrix algebra to decode the message hidden in the given matrices. As you have correctly mentioned, the encoded matrix, U, is the product of (X+Y)^T, where X and Y represent the matrices given in the problem.

To find the real message, you will need to use the inverse of the matrix (X+Y)^T. In matrix algebra, the inverse of a matrix is denoted by A^-1 and it is defined as the matrix that, when multiplied by A, gives the identity matrix I.

To find the inverse of a matrix, you can use the following formula:

A^-1 = (1/|A|) * adj(A)

Where |A| represents the determinant of the matrix A and adj(A) represents the adjugate of the matrix A.

Once you have the inverse of (X+Y)^T, you can multiply it with the encoded matrix U to get the original message. The process of multiplying matrices is known as matrix multiplication and it follows the rule of "row times column".

I hope this helps you in decoding the message. If you need further assistance, please do not hesitate to reach out to your teacher or a tutor for additional support. Good luck!