In the following problems, the letters A to Z correspond to the numbers 1 to 26, as shown below, and a space is represented by the number 27.

Table 2
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
M |

1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |

N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |

14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |

In the next two problems, use the matrix A, given below, to encode the given messages.

A
=
3
2
1
1
A
=
3
2
1
1
size 12{A= left [ matrix {
3 {} # 2 {} ##
1 {} # 1{}
} right ]} {}

In the two problems following, decode the messages that were encoded using matrix A.

Make sure to consider the spaces between words, but ignore all punctuation. Add a final space if necessary.

Encode the message: WATCH OUT!

712466237835873611447712466237835873611447 size 12{ left [ matrix {
"71" {} ##
"24"
} right ] left [ matrix {
"66" {} ##
"23"
} right ] left [ matrix {
"78" {} ##
"35"
} right ] left [ matrix {
"87" {} ##
"36"
} right ] left [ matrix {
"114" {} ##
"47"
} right ]} {}

(74)
Encode the message: HELP IS ON THE WAY.

Decode the following message:

64 23 102 41 82 32 97 35 71 28 69 32

Decode the following message:

105 40 117 48 39 19 69 32 72 27 37 15 114 47

In the next two problems, use the matrix B, given below, to encode the given messages.

B
=
1
0
0
2
1
2
1
0
−
1
B
=
1
0
0
2
1
2
1
0
−
1
size 12{B= left [ matrix {
1 {} # 0 {} # 0 {} ##
2 {} # 1 {} # 2 {} ##
1 {} # 0 {} # - 1{}
} right ]} {}

In the two problems following, decode the messages that were encoded using matrix
BB size 12{B} {}.

Make sure to consider the spaces between words, but ignore all punctuation. Add a final space(s) if necessary.

Encode the message using matrix
BB size 12{B} {}:

LUCK IS ON YOUR SIDE.

125191167219951414105−111587−3279118467−23125191167219951414105−111587−3279118467−23 size 12{ left [ matrix {
"12" {} ##
"51" {} ##
9
} right ] left [ matrix {
"11" {} ##
"67" {} ##
2
} right ] left [ matrix {
"19" {} ##
"95" {} ##
"14"
} right ] left [ matrix {
"14" {} ##
"105" {} ##
- "11"
} right ] left [ matrix {
"15" {} ##
"87" {} ##
- 3
} right ] left [ matrix {
"27" {} ##
"91" {} ##
"18"
} right ] left [ matrix {
4 {} ##
"67" {} ##
- "23"
} right ]} {}

(75)
Encode the message using matrix
BB size 12{B} {}:

MAY THE FORCE BE WITH YOU.

Decode the following message that was encoded using matrix B:

8 23 7 4 47 –2 15 102 –12 20 58 15 27 80 18 12 74 –7

Decode the following message that was encoded using matrix B:

12 69 –3 11 53 9 5 46 –10 18 95 –9 25 107 4 27 76 22 1 72 –26

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