Let A be a 2×2 matrix. Prove that if Av1=λ1v1 and Av2=λ2v2 for distinct reals λ1 and λ2 and nonzero vectors v1 and v2, then both columns of A−λ1I is a multiple of v2.
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Let A be a 2×2 matrix. Prove that if Av1=λ1v1 and Av2=λ2v2 for distinct reals λ1 and λ2 and nonzero vectors v1 and v2, then both columns of A−λ1I is a multiple of v2.