How can Bob decrypt the message?
Bob can divide the encrypted message into smaller vectors of 3 elements each. Then, multiply each of these vectors by the inverse of the encryption matrix and reassemble the resulting vectors into the original matrix.
Can Eve decrypt the message without finding the inverse of the secret matrix?
I am not sure. Mimi said something about how easy it was to decrypt this type of encryption method. She said something about being able to decrypt it by knowing very little information about the message. I think that if eve figures out one of the elements in the matrix, she can pretty much recover the whole message.
What is the decrypted message corresponding to (2,23,3)?
By applying linearity principles we know that
$ \ [2,23,3] = a[2,0,0] + b[0,1,0] + c[0,0,3] $
which yields
$ \ 2 = 2a, 23 = b, 3=3c $
We then apply this coefficients together with the linearity principle stated above to the encrypted message
$ \ 1[1,0,4] + 23[0,1,0] + 1[1,0,1] $
Which yields
$ \ [1+1, 23, 4+1] = [2,23,5] $
[2, 23, 5] corresponds to BWE
