is not invertible iff its row echelon form has at least one null row.
We haven't learned what a determinant is in my linear algebra class, but I should know if a matrix is non-singular/invertible in order to infer if it has a unique solution or not for an upcoming midterm. Any methods that do not include finding the matrix's determinant? Thanks in advance.
Right.
RightThat would imply that the homogeneous system has a nontrivial solution,
Better: if a system with n equations and n unknowns has infinitely many solutions, the corresponding matrix is not invertible.Since a system of equations with infinitely many solutions is not invertible.