Linear Algebra · Advanced · 7 min
Row reduction
Elimination simplifies equations while preserving their simultaneous solutions.
WHAT HAPPENS IF…How do 0=0 and 0=1 differ?
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Subtracting a multiple of one equation from another is reversible, so it preserves the solution set. In the unique example, eliminating and scaling gives y=2 and then x=1. A zero row 0=0 adds no restriction; a row 0=1 is a contradiction. Every scaling used here is nonzero.
A detail that matters
A zero coefficient row does not always mean infinitely many solutions; its augmented entry matters.
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