Tag Archives: 장경석

Concluding 2011 Fall

Thanks all for participating POW actively. Here’s the list of winners:

1st prize: Jang, Kyoungseok (장경석) – 2011학번

2nd prize: Suh, Gee Won (서기원) – 수리과학과 2009학번

3rd prize: Kim, Bumsu (김범수) – 수리과학과 2010학번

4th prize: Park, Seungkyun (박승균) – 수리과학과 2008학번

5th prize: Park, Minjae (박민재) – 2011학번

Congratulations! As announced earlier, we have nicer prize this semester – iPad 16GB for the 1st prize, iPod Touch 32GB for the 2nd prize, etc.

장경석 (2011학번) 28 pts
서기원 (2009학번) 27 pts
김범수 (2010학번) 22 pts
박승균 (2008학번) 14 pts
박민재 (2011학번) 13 pts
강동엽 (2009학번) 11 pts
김태호 (2011학번) 9 pts
김원중 (2011학번) 3 pts
곽영진 (2011학번) 3 pts
조상흠 (2010학번) 3 pts
라준현 (2008학번) 3 pts
배다슬 (2008학번) 3 pts
이재석 (2007학번) 3 pts
최민수 (2011학번) 3 pts
문상혁 (2010학번) 2 pts
박상현 (2010학번) 2 pts

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Solution: 2011-14 Invertible matrices

For a positive integer n>1, let f(n) be the largest real number such that for every n×n diagonal matrix M with positive diagonal entries, if tr(M)<f(n), then M-J is invertible. Determine f(n). (The matrix J is the square matrix with all entries 1.)

The best solution was submitted by Kyoungseok Jang(장경석), 2011학번. Congratulations!

Here is his Solution of Problem 2011-14.

Alternative solutions were submitted by 곽영진 (2011학번, +3), 박민재 (2011학번, +3), 라준현 (수리과학과 2008학번, +3), 서기원 (수리과학과 2009학번, +3), 배다슬 (수리과학과 2008학번, +3), 김범수 (수리과학과 2010학번, +3), 어수강 (서울대학교 수리과학부 대학원, +3), 조위지 (Stanford Univ. 물리학과 박사과정, +3).

PS. There were solutions without computing the determinant. Here is a Solution of Problem 2011-14 by 김범수.

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