Part 1
Bob can decrypt the message by multiplying 3 letter sequences by the inverse of the encryption matrix.
Part 2
Because this encryption is linear, Eve doesn't need to know the inverse to decrypt messages. She can write any unknown message as linear multiples of the message she knows. This is easier done then said, see the example in part 3.
Part 3
<2,23,3> can be written as 1<2,0,0> + 23<0,1,0> + 1<0,0,3>
Since we know the inputs that yield the vectors <2,0,0> , <0,1,0> , and <0,0,3>, linearity says the corresponding input is:
- 1<1,0,4> + 23<0,1,0> + 1<1,0,1>
which simplifies to <2,23,5>, or BWE
