You are close to correct. If the rank of a matrix is less than the number of unknowns it implies either an infinite number of solutions or zero solutions.
Going through a textbook and I come across the term 'rank' of a matrix.
I haven't come across this term before, am I right in thinking that the rank of an augmented matrix (that has been reduced) is the number of non-zero rows. And if the rank of a matrix < the number of unknowns => infinite number of solutions.
Sorry if it seems like a basic question, just don't want to go any further with wrong ideas