- #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

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- Thread starter EvLer
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- #1

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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.

Thanks

- #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

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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.

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.

ps: sorry, perhaps I made a mistake: 6 equations IN 5 unknowns.

- #5

HallsofIvy

Science Advisor

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That was what everyone assumed you meant, that is what radou gave.

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