# 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 $$v_2$$.

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