System of equations

  • Thread starter phymatter
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  • #1
phymatter
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if in a system of linear equations we have lesser number of linear equations than the number of variables then is the number of solutions set to the system always infinite ?
 
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  • #2
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Not necessarily.

For example, in this system the solution set is empty.
x + y + z = 2
x + y + z = 3

Geomatrically, this system represents two planes in three-dimensional space. The planes are parallel and don't intersect.
 

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