1. Yes, Bob must first use his matrix arithmatic skills to find the inverse of the secret matrix. Then, he must multiply the inverse of the secret message times each row. Finally, replacing the numbers with the corresponding alphabetic letters and leaving 0's as a space, he will have decoded the message.
2. Where their is a will, their is a way is what I always say. I do not specifically know how to manipulate the vectors without finding the inverse, but I'm sure it can be done. How many tries did it take Edison to light the lightbulb? On the other hand it would be the easiest for her to simply find the inverse of the secret matrix to spy on Alice & Bob's secret mathmatical romance...
3. (2,23,3) --> BWE
>> x=[-2/3 0 2/3
0 1 0
4 0 -1]
xprime=x^-1
p=[2
23
3]
codedmessage = xprime*p
x =
-0.6667 0 0.6667
0 1.0000 0
4.0000 0 -1.0000
xprime =
0.5000 0 0.3333
0 1.0000 0
2.0000 0 0.3333
p =
2
23
3
codedmessage =
2
23
5
