# How to Determine if a Linear System is Consistent or Inconsistent?

In this video, we show how to determine if a linear system is consistent or inconsistent. In fact, if the rank of coefficient matrix equals the rank of argument matrix, the system is consistent. Otherwise, if the rank of coefficient matrix is less than the rank of argument matrix, the system is inconsistent.

The rank of a matrix is the number of nonzero rows in the row echelon form form the matrix.