Does it mean that there is at least one non-zero coefficient? That the solution set does not include the zero vector? That the the equation is non-homogenous? I am asking because the phrase is used in my linear algebra text (Friedberg, Insel, Spence.)
[Math] a “nonzero equation”
linear algebraterminology
Best Answer
In row echelon form, the rank is exactly the number of nozero rows. Therefore (a) indicateds that "nonzero equation" is one where at least one coefficient (or the right hand side) is nonzero. Note that $\operatorname{rank}(A)=\operatorname{rank}(A|B)$ implies that there are no contradictory equations.