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kirchoff's rules and linear dependence



I teach my high school gifted and talented physics class how to use a graphing calculator and matrix algebra to solve circuit problems involving kirchoff's rules. The typical "book problem" has three different currents in it so the students come up with three equations: a "junction rule" equation and two "loop rule" equations.

Today a student used three loop rule equations and was puzzled as to why her calculator returned an error, as was I until I realized that the three equations were not linearly independent.

I would like to talk to the students about this tomorrow but
a) I can't convince myself why the three loop rule equations are not linearly independent

b) I am not sure how to (or if I should) explain this to HS juniors who probably haven't learned much about linear algebra.

Thanks as always

Justin Parke
Oakland Mills High School
Columbia, MD