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However the set is comprised of subsets of vectors, where the vectors of each subset belong to the same eigenvalue. For example, in a 7-square matrix, ##v_1, v_2, v_3## belong to ##λ_1##, ##v_4, v_5## belong to ##λ_2## and ##v_6, v_7## belong to ##λ_3##. How do we prove the vectors are still linearly independent?