Homogenious equations

[phymatter]

if we have same number of linearly independent homogenious equations as the number of variables , then how many solutions will we get apart from the trivial solution ?

 

[AlephZero]

If you are talking about linear equations that are linearly indepdent, the only solution is the trivial one with all the variables equal to zero.

For nonlinear equations, anything might happen, depending on the particular equations.

 

[phymatter]

thanks alephzero !!