Suppose that a homogeneous system of equations has a unique solution.
Give an example of such a system by writing its augmented matrix in reduced row echelon form.
Write just the coefficient matrix for the example you gave in the previous part. What can you say about the pivot positions in the coefficient matrix? Explain why your observation must hold for any homogeneous system having a unique solution.
If a homogenous system of equations has a unique solution, what can you say about the number of equations compared to the number of unknowns?