Question

Need Help with decoding matrix using alphabet table.
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.

Answer 1

I assume C is a 2x2 matrix?

Answer 2

Here is a site that shows how to find the inverse of a 2x2 matrix
http://www.mathwords.com/i/inverse_of_a_matrix.htm

Answer 3

I don't understand

Answer 4

\[C=\left[\begin{matrix}1 & -2 \\ -3 & 7\end{matrix}\right]\]
The inverse is
\[C^{-1}= \left[\begin{matrix}7 & 2 \\ 3 & 1\end{matrix}\right]\]

You can check by multiply C * C inverse and you will get I (The identity matrix)

Answer 5

if we call your message m, and the encoded message e
they did
C m = e
if you multiply both sides by \(C^{-1}\) you get
m = \(C^{-1}\)e

that says to decode your message, multiply it by C inverse

Answer 6

OK, but first can you multiply C * C inverse ?