Write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or infinitely many solutions.
The Attempt at a Solution
I saw right away that Row 3 and Row 2 are the same equation, off by a factor of 2. Because of this, I was able to make the matrix with a zero row for Row 2, which shows that row 2 and row 3 are linearly dependent. However, my question arises here. I know that a zero row and linear dependence of these two equations means that there is either 0 solutions or infinitely many solutions. Since they are linearly dependent, there is not one unique solution. However, How can I tell whether there is 0 solutions or infinitely many?