• An underdetermined system has fewer equations than variables.

  • In this case, we can only have no solution or infinitely many solutions. A unique solution is not an option.

• An overdetermined system has more equations than variables.

  • In this case, we can have no solution, infinitely many solutions, or a unique solution. (There are no restrictions.)

• The number of equations is the number of rows in the augmented matrix.

• The number of variables is the number of columns in the coefficient matrix.

Columns in the row-reduced matrix that are not unit columns correspond to variables that should be assigned parameters.