Practice question · True or false
A consistent linear system with more unknowns than equations always has infinitely many solutions.
Hints
- Count the free variables.
- Fewer equations than unknowns leaves at least one free.
Show the answer
True
Why
True. Each equation can pin at most one variable, so with more unknowns than equations at least one stays free, and a free variable in a consistent system generates infinitely many solutions. The 'consistent' qualifier matters: without it the system may have none at all.
Practise Systems of Linear Equations
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