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Hey guys I was wondering if someone could tell me what each of the different scenarios of a guassian elimination mean. (3 equations)

e.g. one row of $0$ means that its a line in $R^3$ (I think)

What would the result of the elimination look like if it was a point in $R^3$?

What would the result of the elimination look like if it was a plane in $R^3$? $2$ of the three equations being $0=0$?

What would the result of the elimination look like if it was empty? It being entirely of $0s$?

Doing revision for a test and this is the only question I could not understand, thanks for any help.

Ski Mask
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Mathlete
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    Each row represents the equation of a plane in 3D. One row of 0's after elimination leaves 2 planes left (or an inconsistent equation with 3 zeros and a non-zero fourth digit in the rightmost column). What can happen with 2 planes? Two rows of zeros leaves one plane left. The system can never consist of entirely zeros – Paul Jan 11 '18 at 11:52

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