Row Reduction

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We row reduce a matrix by performing row operations, in order to find a simpler but equivalent system for which the solution set is easily read off.

A central idea in solving systems of equations is the notion of equivalence.

Two systems of equations of the same dimensions are equivalent if they have the same set of solutions.

Given a system of equations, how can we find its solution set? The answer is by finding a simpler but equivalent system for which the solution set is easily read off. The method used for finding this simpler system is called row reduction.