1) Do equations with 3 variables require at least 3 equation for us to solve without any dependent variable?2) if two equations of such kind equate to zero for eg: a − b + 2 c = 0 and 3 a + b + c = 0. Then using the matrice ,there is a method to solve them...explain that method.is there a proof or is it related to Gaussian method which is out of my scope?

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1) Do equations with   3 variables require at least   3 equation for us to solve without any dependent variable?2) if two equations of such kind equate to zero for eg:   a  −  b  +  2  c  =  0 and   3  a  +  b  +  c  =  0. Then using the matrice ,there is a method to solve them...explain that method.is there a proof or is it related to Gaussian method which is out of my scope?

Nirdaciw3 · Accepted Answer

1) For linear equations over the reals, yes, you need as many equations as variables. In the usual case you will have a unique solution. For equations over the naturals, you can sometimes get by with less. Also consider       x    2    +      y    2    +      z    2    =  0 That looks like one equation, but there is only one solution in the reals for three variables.

Holetaug · Accepted Answer

2) The matrix method works fine with two equations with no constant. You may have equations that are inconsistent or duplicative, but that can happen with a constant as well.

1) Do equations with 3 variables require at least 3 equation for us to solve without any

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