# Word Matrices, Level 2

This puzzle is based on NeedAName's recent puzzle, Determinant of Word Matrix.

The challenge:

Create a $3\times3$ matrix of distinct letters (i.e. no repeated letters) with no vowels in the middle row such that the six terms generated when calculating the determinant form valid English words.

Words are considered valid if and only if they are English words found on Dictionary.com (not including (pre/suf)fixes, abbreviations, acronyms, proper names, etc.).

For example, with a simple $2\times2$ matrix $\begin{bmatrix}O & I\\N & R\end{bmatrix}$, the determinant is $OR-IN$.
This forms two 2-letter words.

With a $3\times3$ matrix $\begin{bmatrix} A & B & C\\D & E & F\\G & H & I \end{bmatrix}$ you will end up with six 3-letter words:

$AEI + BFG + CDH -CEG - BDI - AFH$.

Since the actual determinant doesn't matter, the easiest way to think of this is as a $3\times5$ matrix with the first two columns repeated:

$\begin{bmatrix} A & B & C & A & B\\D & E & F & D & E\\G & H & I & G & H \end{bmatrix}$

Then you just need to make sure all the intact diagonals $\searrow$ and $\swarrow$ are valid words.

• +1 for superior formatting! I should have you organize my puzzles before posting them :) Sep 22 '15 at 17:47
• Haven't you over-complicated the puzzle? The last para is enough to understand the question by itself. Sep 22 '15 at 18:10
• @ghosts I considered that, but it just seems really arbitrary to ask for a $3\times5$ matrix with certain repeated columns that fits a certain pattern. I thought keeping the determinant explanation in there would help people understand where the idea came from, so it's not quite so arbitrary. Sep 22 '15 at 18:56

$\begin{bmatrix} A & I & O\\F & D & C\\E & T & S \end{bmatrix}$ producing the words ADS, ACT, IFS, ICE, OFT, and ODE.