Condition of augmented matrix for solution of equation
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The three types of solution sets:
A system of linear equations can have no solution, a unique solution or infinitely many solutions.
A system has no solution if the equations are inconsistent, they are contradictory. for example 2x+3y=10, 2x+3y=12 has no solution. is the rref form of the matrix for this system. 
The rref of the matrix for an inconsistent system has a row with a nonzero number in the last column and 0's in all other columns, for example�� 0 0 0 0 1. If the augmentation bar is present, the 1 is to the right of the bar and only 0's are on the left.
The number of variables is always the number of columns to the left of the augmentation bar.
A system has a unique solution when it is consistent and the number of variables is equal to the number of nonzero rows. If the rref of the matrix for the system is ,
the solution is the single point ( 2, 1, 3 ) or x=2, y=1, z=3
A system of linear equations can have no solution, a unique solution or infinitely many solutions.
A system has no solution if the equations are inconsistent, they are contradictory. for example 2x+3y=10, 2x+3y=12 has no solution. is the rref form of the matrix for this system. 
The rref of the matrix for an inconsistent system has a row with a nonzero number in the last column and 0's in all other columns, for example�� 0 0 0 0 1. If the augmentation bar is present, the 1 is to the right of the bar and only 0's are on the left.
The number of variables is always the number of columns to the left of the augmentation bar.
A system has a unique solution when it is consistent and the number of variables is equal to the number of nonzero rows. If the rref of the matrix for the system is ,
the solution is the single point ( 2, 1, 3 ) or x=2, y=1, z=3
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