(New page: == Problem #1 == Bob can decrypt the message by splitting the encrypted text into a 3x3 matrix, then multiplying the encrypted by the inverse of the secret message matrix. The secret mess...) |
(→Problem #3) |
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0 & 1 & 0 \\ | 0 & 1 & 0 \\ | ||
0 & 0 & 3 | 0 & 0 & 3 | ||
| + | \end{bmatrix}</math> | ||
| + | |||
| + | <math> | ||
| + | \begin{bmatrix} | ||
| + | 2 & 0 & 0 \\ | ||
| + | 0 & 1 & 0 \\ | ||
| + | 0 & 0 & 3 | ||
| + | \end{bmatrix} | ||
| + | x | ||
| + | \begin{bmatrix} | ||
| + | 1 & 0 & 4 \\ | ||
| + | 0 & 1 & 0 \\ | ||
| + | 1 & 0 & 1 | ||
| + | \end{bmatrix}^{-1} | ||
| + | = \begin{bmatrix} | ||
| + | \frac{-2}{3} & 0 & \frac{2}{3} \\ | ||
| + | 0 & 1 & 0 \\ | ||
| + | 4 & 0 & -1 | ||
\end{bmatrix}</math> | \end{bmatrix}</math> | ||
Revision as of 21:26, 17 September 2008
Problem #1
Bob can decrypt the message by splitting the encrypted text into a 3x3 matrix, then multiplying the encrypted by the inverse of the secret message matrix. The secret message is also a 3x3 matrix.
Problem #2
No she cannot figure out the secret message without finding the inverse of the secret matrix. As of right now, I cannot think of another way to decrypt the message without using the inverse of the matrix.
Problem #3
Step by Step equations to finding the ecrypted message:
$ \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} x \begin{bmatrix} 1 & 0 & 4 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 3 \end{bmatrix} $
$ \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 3 \end{bmatrix} x \begin{bmatrix} 1 & 0 & 4 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix}^{-1} = \begin{bmatrix} \frac{-2}{3} & 0 & \frac{2}{3} \\ 0 & 1 & 0 \\ 4 & 0 & -1 \end{bmatrix} $
