homogeneous equations revisited denitions criteria for in dependence independence versus dependence linear dependence and independence a havens department of mathematics university of massachusetts amherst february 7 2018 a havens linear ...
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...Homogeneous equations revisited denitions criteria for in dependence independence versus linear and a havens department of mathematics university massachusetts amherst february outline anewperspective on ax dependency relations from nontrivial solutions non triviality special cases low dimensions the theory variables essential ideas new perspective combinations equal to reconsider meaning solution x rn system rm if columns are then this means there is n combination where at least one coecients nonzero i now could be uninteresting e g matrix full only zeroes but we know examples systems an example with z has innitely many corresponding line intersection three planes...