Is the Jacobian Matrix of This Function Symmetric?

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In summary, "Can You Solve This Week's Problem?" is a weekly challenge where participants are given a problem to solve using their scientific knowledge and skills. To participate, you can visit the website of the presenting publication or organization and submit your solution according to their instructions. The prize for solving the problem may vary and can range from monetary rewards to recognition or opportunities to present at conferences. The difficulty of the problems can vary greatly, from basic scientific knowledge to advanced skills. Collaboration may or may not be allowed, depending on the discretion of the presenting publication or organization.
  • #1
Chris L T521
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Here's this week's problem!

-----

Problem: Let $J$ denote the Jacobian matrix. Show that if $f$ has continuous second-order partial derivatives and $\mathbf{F}(\mathbf{x}) = (Jf(\mathbf{x}))^T$, then $J\mathbf{F}(\mathbf{x})$ is a symmetric matrix.

-----Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
 
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  • #2
No one answered this week's problem. Due to recent events, I've been pretty swamped with work/GRE prep (taking the exam next Saturday, 10/13); hence, I don't have a solution ready at this time. I'll update this post with one sometime this week.
 

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