What does a row of 0 's in an augmented matrix tell you
about the system of equations it is representing?
The system is inconsistant and has a unique
solution.
The system is inconsistant and has an infinite
number of solutions.
The system has no solutions.
The system is consistant and has an infinite
number of solutions.
The system is consistent and has a unique solution.

A row of zeros in an augmented matrix can tell you a lot about the system of equations it represents! Specifically, if this row corresponds to an equation that simplifies to 0 = 0, it indicates that the system has dependent equations, often suggesting it may have infinitely many solutions if other equations also align. However, if the augmented part of the row leads to a contradiction (like 0 = 1), then the system is inconsistent with no solutions.

To visualize this, think of a system with three variables where one equation essentially disappears, leaving you with two equations in three unknowns. In such cases, you often find that you can freely choose one variable, leading to infinitely many solutions along a line in space. This is a common scenario in linear algebra!