Let A=(aij) be an n×n matrix of complex numbers such that \(\displaystyle\sum_{j=1}^n |a_{ij}|<1\) for each i. Prove that I-A is nonsingular.

The best solution was submitted by  Sung-Min Kwon (권성민), 2009학번. Congratulations!

Here is his Solution of Problem 2010-2.

Alternative solutions were submitted by 라준현 (수리과학과 2008학번, +3), 서기원 (2009학번, +3), 임재원 (2009학번, +3), 정성구 (수리과학과 2007학번, +3).