Suppose a group \(G\) has a finite index subgroup that maps onto the free group of rank 2. Show that every countable group can be embedded in one of the quotient groups of \(G\).

The best solution was submitted by 하석민 (수리과학과 2017학번). Congratulations!

Here is his solution of problem 2019-16.

Let \( A, B \) be \( n \times n \) Hermitian matrices. Find all positive integer \( n \) such that the following statement holds:

“If \( AB – BA \) is singular, then \( A \) and \( B \) have a common eigenvector.”

The best solution was submitted by 채지석 (수리과학과 2016학번). Congratulations!

Here is his solution of problem 2019-14.

A similar solution was submitted by 하석민 (수리과학과 2017학번, +3). Late solutions are not graded.