We want to write the uncoded 1* 3 row matrices for the message.
LOOK OUT BELOW
We can start by recalling that matrix multiplication can be used to encode and decode messages. Let's recall which numbers are assigned to which letter in the alphabet. Remember that blank space corresponds to 0.
Code
0=
9=I
18=R
1=A
10=J
19=S
2=B
11=K
20=T
3=C
12=L
21=U
4=D
13=M
22=V
5=E
14=N
23=W
6=F
15=O
24=X
7=G
16=P
25=Y
8=H
16=Q
26=Z
Now, we can partition our message (including blank spaces) into groups of three.
1{\text{LOOK OUT BELOW} \\ \Updownarrow \\ L&O&O
K& &O U&T&\\ B&E&L O&W&}
Finally, we can use our table to rewrite each group as a 1* 3 matrix.
Group of Three Letters
Uncoded Row Matrix
L&O&O
12&15&15
K& &O
11&0&15
U&T&
21&20&0
B&E&L
2&15&12
O&W&
15&23&0
First, we can look at the given encoding matrix.
2&-2 & 0 3&0&- 3 - 6& 2&3
We want to encode the message from Part A using the given encoding matrix. Let's consider the uncoded row matrices from Part A!
1{12&15&15 11&0&15 21&20&0
\\ 2&5&12 15&23&0}
Now, we can multiply each of the uncoded row matrices by the encoding matrix to get a corresponding coded matrices. Let's start with the first uncoded row matrix.
