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 than 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 Eve knows the inputs that yield the vectors <2,0,0> , <0,1,0> , and <0,0,3>, by linearity the input for the encrypted message is:
- 1<1,0,4> + 23<0,1,0> + 1<1,0,1>
which simplifies to <2,23,5>, or BWE
