When put into rref from i get
Now this says 0 = 5, so presumably this system is inconsistant as 0 in my experiance doesn't equal 5.
Is there any way to find out if the system is inconsistant before i do 5 or more elementary row operations, which could be vital time wasted in an exam?
Thanks
Why did you have to do 5 elementary operations? After the very first one, when you bring the first column (below the entry 1-1) to zero, the second and third rows are identical EXCEPT for the right most entry, which in the 2nd row is -2 and in the 3rd row is 3.
This already tells you the system is inconsistent since in the next step you will substract row 3 from row 2 and all the entries BUT the last one at the right in the 3rd row will vanish.
This says that 0*x1 + 0*x2 + 0*x3 + 0*x4 = 5, which of course is nonsense (unless you're working with a field of characteristic 5. If you don't understand this remark erase it right now from your brain: it isn't important for you right now)
Thus at most two steps, thought the result is visible already after the first one.
Tonio