 Let's examine one important situation that may arise from our process of row reduction. And that's the following. Suppose I have an augmented coefficient matrix for a system of equations, and after row reduction we end up with a row consisting of all zeros, except for the last entry, which is not equal to zero. What does this tell us? So in this case, suppose I have my augmented coefficient matrix, and we row reduce it, and we end up with a matrix where this last row here is all zeros, and there's a number at the end, so how about the number five? Now remember, every row of a matrix corresponds to a row of an equation. So this last row of zeros is going to correspond to the equation zero x one plus zero x two, and so on, equal to five. And after all the dust settles in this equation, we find that zero is equal to five. Now unless you're bragging about the number of people who came to your party, zero is not equal to five. This is actually impossible. And what this tells us is that our original system of equations has no solution. And again, it's important that while we can start by looking at an example, we don't want to end there, and if this constant is any other number, we still get the same result, which is to say an impossibility and no solution to our original system of equations.