First Principles AI

Solution

Given coded matrix:

C=\begin{bmatrix}11&25&22\\20&10&14\\43&41&41\end{bmatrix}

and encoding matrix:

A=\begin{bmatrix}1&1&-1\\1&0&1\\2&1&1\end{bmatrix}

Decoding uses:

P=A^{-1}C

Compute $A^{-1}$ :

A^{-1}=\begin{bmatrix}1&2&-1\\-1&-3&2\\-1&-1&1\end{bmatrix}

Now:

P=A^{-1}C= \begin{bmatrix}8&4&9\\15&27&18\\12&6&5\end{bmatrix}

Interpret numbers ( $1\to A,\dots,26\to Z$ , $27\to$ space):

So the decoded message is:

\boxed{\text{HOLD FIRE}}