I just noticed a fact that I hadn't seen before, which I'll illustrate with two examples:

\[ \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix} = 0 \]

\[ \begin{vmatrix} 0 & 1 & 2 \\ 3 & 6 & 9 \\ 12 & 16 & 20 \end{vmatrix} = 0 \]

What's the pattern?

Rahul Narain
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@christianp Any three arithmetic progressions are linearly dependent?

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