Use the given encoding matrix A to solve the problem. A message has been encoded

Question

Use the given encoding matrix A to solve the problem. A message has been encoded and the matrix which the receiver gets is shown to the right. The encoding matrix A which was used to encode the message is A = [0 2 3 1]. Find the decoding matrix A^-1, and use it [3 11 90 70 45 65 54 60 66 82 21 17 60 30 6 4 15 29 120 78] to decode the message. Assume that the numerical assignment used was a = 1, b = 2, z = 26, space = 30, period = 40, and apostrophe = 60. DRINK ENOUGH MILK EAT YOUR BROCCOLI EAT YOUR VEGETABLES DRINK ENOUGH COKE

Explanation / Answer

We have ,

A = 0 2

3 1

So , A^-1 = -1/6 1/3

1/2 0

Let M be the matrix , and X be your original message

encoding has been by doing the multiplication

XA=M

So your original message will be

X = MA^-1

Multiplying we get final result as

X =

5 1

20 30

25 15

21 18

30 22

5 7

5 20

1 2

12 5

19 40

therefore your message will be

EAT YOUR VEGETABLES

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