Let \(A\) be a \(2\times 2\) matrix. Prove that if \(Av_1=\lambda_1v_1\) and \(Av_2=\lambda_2v_2\) for distinct reals \(\lambda_1\) and \(\lambda_2\) and nonzero vectors \(v_1\) and \(v_2\), then both columns of \(A-\lambda_1 I\) is a multiple of \(v_2\).
The best solution was submitted by Lee, Jongwon (이종원, 수리과학과 2014학번). Congratulations!
Here is his solution of problem 2018-12.
Alternative solutions were submitted by 고성훈 (2018학번, +3), 권홍 (중앙대 물리학과, +3), 길현준 (2018학번, +3), 김태균 (수리과학과 2016학번, +3), 이본우 (수리과학과 2017학번, +3), 채지석 (수리과학과 2016학번, +3), 한준호 (수리과학과 2015학번, +3).