Routh Stability criterion

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To check for the numbers of poles lying in the right side of the s-plane in a causal system, why do we check for the sign change only in first column ?

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Have a look at: wwwhome.math.utwente.nl/~meinsmag/reports/routh_tcns.pdf

"Elementary proof of the Routh-Hurwitz test" by Gjerrit Meinsma