System of linear equations

  • Thread starter EvLer
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  • #1
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Homework Statement



is every system of 6 equations and 5 unknowns consistent?

I think that not every one is consistent because after Gaussian elimination you may arrive at equation where 0=1, but I want a sure confirmation.
Thanks
 

Answers and Replies

  • #2
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is every system of 6 equations and 5 unknowns consistent?

I think that not every one is consistent because after Gaussian elimination you may arrive at equation where 0=1, but I want a sure confirmation.
What does it mean for a system of linear equations to be consistent? Does your answer agree with the definition?
 
  • #3
radou
Homework Helper
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A trivial example:

x1 + x2 + x3 + x4 + x5 = 1
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0

Does this system have a solution?

Edit: I forgot to add the 6th equation. The question remains unchanged.
 
Last edited:
  • #4
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thanks.
ps: sorry, perhaps I made a mistake: 6 equations IN 5 unknowns.
 
  • #5
HallsofIvy
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That was what everyone assumed you meant, that is what radou gave.
 

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