Question

use [1 -2 -3 7] encode the phrase "ONE QUESTION TO GO"
1 = A
2 = B
3 = C
4 = D
5 = E
6 = F
7 = G
8 = H
9 = I
10 = J
11 = K
12 = L
13 = M
14 = N
15 = O
16 = P
17 = Q
18 = R
19 = S
20 = T
21 = U
22 = V
23 = W
24 = X
25 = Y
26 = Z

The matrix c= [1 -2 -3 7] was used to encode a phrase to [7 -28 -25 -35 -2 -21 107 90 123 17] Find c^-1 and use it to decode the matrix.

PLEASE HELP I DONT UNDERSTAND THIS AT ALL

Answer 1

So I guess c is a 2 by 2 matrix or a 1 by 4 matrix?

Answer 2

2 by 2

Answer 3

So you can find the inverse of c?

Answer 4

\[(\left[\begin{matrix}a & b \\ c & d\end{matrix}\right])^{-1}=\frac{1}{ad-bc} \left[\begin{matrix}d & -b \\ -c & a\end{matrix}\right]\]

Answer 5

give me a min

Answer 6

1/1 [ 7 -3 -2 1] ??

Answer 7

@freckles

Answer 8

It looks like you didn't change the sign of -3 and -2 but you switch their places...

Answer 9

wait so they would be positive...did i even do that right sorta?

Answer 10

\[(\left[\begin{matrix}a & b \\ c & d\end{matrix}\right])^{-1}=\frac{1}{ad-bc} \left[\begin{matrix}d & -b \\ -c & a\end{matrix}\right] \] \[
(\left[\begin{matrix}1 & -2 \\ -3 & 7\end{matrix}\right])^{-1}=\frac{1}{(1)(7)-(-2)(-3)} \left[\begin{matrix}7 & -(-2) \\ -(-3) & 1\end{matrix}\right] \]

Answer 11

I will let you simplify that.

Answer 12

When you are done I'm assuming that one matrix like in your last sentence is a 2 by 5 matrix
So you are going to that your inverse of c and multiply the 2 by 5 matrix

Answer 13

This will give us what we need to decode the last matrix

Answer 14

We will encode the "ONE QUESTION TO GO" when we are done decrpying the 2 by 5 matrix

Answer 15

alright. is this an easier way of figuring it out ?

Answer 16

? Aren't we suppose to decode that last matrix in your last sentence?

Answer 17

yes

Answer 18

Ok so we have to find the inverse of c
have you done that yet?

Answer 19

I gave you the setup and just asked you to simplify

Answer 20

You are going to multiply inverse of c times that 2 by 5 matrix

Answer 21

http://aix1.uottawa.ca/~jkhoury/cryptography.htm
here is an example of what I interpreted that we are doing

Answer 22

They used a 3 by 3 key instead of a 2 by 2 key

Answer 23

But to decode something you do need the matrix's inverse whether it be a 3 by 3 or a 2 by 2 key

Answer 24

well that seems to explain it really well

Answer 25

http://www.wolframalpha.com/input/?i=%7B%7B7%2C2%7D%2C%7B3%2C1%7D%7D+times+%7B%7B7%2C-28%2C-25%2C-35%2C-2%7D%2C%7B-21%2C107%2C90%2C123%2C17%7D%7D
So it this that 2 by 5 matrix you have written there?

Answer 26

yes it is

Answer 27

So after you perform that multiplication
You will use that list list of letters you have above to translate

Answer 28

The only think is the message makes no sense

Answer 29

thing*

Answer 30

i think i was thinking to hard on these two problems and got all confused