# Solution: 2018-12 Property of Eigenvectors

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).

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