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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Ah, now I see how this works. Nice puzzle.

Why did the vector cross the road?

It wanted to be normal.

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**scientia****Member**- Registered: 2009-11-13
- Posts: 224

In general, for , we have

This can be proved by induction. For the inductive step, note that

Hence, for this problem,

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

scientia wrote:

In general, for , we have

This is a very neat formula. It also proves that if

then −1 ∊ *M[sub]n[/sub]*

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