step $1$: vvrite tne message in a matrix:

Message $(M)=($ Hello Sam $)=([H,E,L],[L,O,$ space $],[S,A,M])$

Step $2$: Translate to numbers using the table above, that gives you the Message Matrix:

$([H,E,L],[L,O,$ space $],[S,A,M])=([8,5,12],[12,15,0],[19,1,13])=M$

Step $3.$ A certain Key$($K$)$ Matrix is given. Perform the operation: KM $($that is multiply the key matrix by the Message Matrix,

that gives you the Encoded Matrix:

$KM=C(encoded$ matrix$)$

$If$ the Key Matrix $is$ the following you get: Key$(K)=([-1,0,2$

$2,-9,3$

$5,1,-2])$

Encoded Matrix: $C=([-1,0,2$

$2,-9,3$

$5,1,-2])([8,5,12$

$12,15,0$

$19,1,13])=([30,-3,14$

$-35,-122,63$

$14,38,34])$

Step $4,$ To get from the Encoded Matrix to the real matrix,$\_$you need to know the Inverse Matrix of the Key Matrix.

$M=K^{-1}C$ Question $1$

Now it is your job to decode the following message: Notice you have to split it up in three $33$

matrices:

Coded Matrix: $([501,172,587,75,140,272,498,205,310],[438,169,533,48,131,272,435,215,240],[212,83,259,22,63,134,211,107,110])$

You have the Key Matrix:

$([7,10,15],[4,7,16],[2,3,8])$

Decode the matrix and perform the task. HOW TO ENCRYPT MESSAGES WITH MATRICES

This is how it works:

Step $1$: Write the message in a matrix:

$([H,E,L])$