It's Wednesday, and that means another Advanced Knowledge Problem of the Week. This one should be fine if you know your linear algebra and multivariable calculus.
You can find my solution to the problem after the break.
If you've been enjoying our Problems of the Week of both kinds, you're in for a treat: since the MAA MathFest is this week, we've got a bunch of extra challenges lined up for you. Stay tuned for more information coming this afternoon! If you liked this problem, let us know in the comments!