You can put this solution on YOUR website! Dependent matrix would have a determinant of zero and when you looked at the rows, they would be multiples of each other. The right hand side would also have the same multiplier from line to line.
As an example,
[A]=
[x]=
[b]=
The first equation would be and the second equation would be . So the second equation is twice the first equation. They are the same line.
.
.
.
An inconsistent matrix would also have a determinant of zero but the multiplier to go from one row to the next on the left hand side does not equal to the right hand side multiplier.
Here's an example,
[C]=
[x]=
[b]=
where the equations are and , the lines are parallel.
