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- Remaining equations due to Gauss elimination of a first set of unknowns from an homogeneous linear system

Hi,

I ask for a clarification about the following: consider for instance a 10 x 12 homogeneous linear system and perform Gauss elimination for the first 8 unknowns. Suppose you end up with 5 equations in the remaining 12-8 = 4 unknowns (because in the process of the first 8 unknowns elimination you end up in a raw echelon form with a non-pivot column - basically a free unknown).

For sure the remaining 5 equations are linearly dependent (because of 5 homogeneous equation in 4 unknowns) but my doubt is: for some reason has to be one of the 5 equations identically null (a zero raw) ?

thanks

I ask for a clarification about the following: consider for instance a 10 x 12 homogeneous linear system and perform Gauss elimination for the first 8 unknowns. Suppose you end up with 5 equations in the remaining 12-8 = 4 unknowns (because in the process of the first 8 unknowns elimination you end up in a raw echelon form with a non-pivot column - basically a free unknown).

For sure the remaining 5 equations are linearly dependent (because of 5 homogeneous equation in 4 unknowns) but my doubt is: for some reason has to be one of the 5 equations identically null (a zero raw) ?

thanks

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