I was learning Linear Algebra from Hoffman and Kunze. There the authors prove that for a row reduced echelon matrix with rows r and columns n for a homogeneous system of equations X, if r < n, X has a non-trivial solution, which I understood (substituting, r unknowns with remaining unknowns). However, what would happen in case of
- r = n
- r > n
For r = n, I am guessing it would be trivial solution only as no substitution is possible. Please correct me if wrong.
Best Answer
$Ax=0$ is homogeneous system.It always have trivial solution.If r=n then system will have trivial solution.As $rank(A)\le min{(r,n)}$. Hence r can not be greater than n.