So, I'm gaming the system a bit here, but A2 asks "What is the determinant?", not "Characterize the determinant," or anything vague like that. But they also say "... in some order ...", as if the order doesn't matter to the determinant. The only way that can be true is if the determinant is zero. So now I'm thinking, how can I prove the determinant is zero? Do I need to, or can I just cite the reasoning I just gave? On Tue, Dec 4, 2018 at 11:14 PM Dan Asimov <dasimov@earthlink.net> wrote:

Duh! I could've sworn I included the instruction

----- Calculate the determinant of M. -----

but apparently not.

But that's the problem: Find the determinant of that matrix.

Sorry for the oversight.

—Dan

Allan Wechsler and/or Mike Stay wrote stuff like: -----

...

A2 is really easy!

and

...

I think you left out the punch line.

...

On Tue, Dec 4, 2018 at 5:37 PM Dan Asimov <dasimov@earthlink.net> wrote:

...

questions from the recent Putnam Exam ...

...

----- A2 Let S_1, S_2, ..., S_(2n−1) be the nonempty subsets of {1,2,...,} in some order, and let M be the (2n−1)×(2n−1) matrix whose (i,j)th entry m(i,j) = 0 if S_i ∩ S_j is empty; m(i,j) = 1 otherwise. -----

---

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