Let A and B be n×n matrices over the real field R. Prove that if A+B is invertible, then A(A+B)^{-1}B=B(A+B)^{-1}A.

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Let A and B be n×n matrices over the real field R. Prove that if A+B is invertible, then A(A+B)^{-1}B=B(A+B)^{-1}A.

Good luck with the midterm exam! The next POW problem will be announced on Oct. 30.

Suppose y(x)≥0 for all real x. Find all solutions of the differential equation \(\frac{dy}{dx}=\sqrt{y}\), y(0)=0.

The best solution was submitted by Seong-Gu Jeong (정성구), 수리과학과 2007학번. Congratulations!

Here is his Solution of Problem 2009-18.

There were 2 incorrect submissions.

Suppose y(x)≥0 for all real x. Find all solutions of the differential equation \(\frac{dy}{dx}=\sqrt{y}\), y(0)=0.

This week no problem will be posted due to Chuseok. Enjoy the holiday and see you next week!