Question

Please, give me a counterexample for this:
A linear system is consistent if and only if there are free variables in the row-echelon form of the corresponding augmented matrix

Answer 1

take system of equations wid uniq solution, then we wont be having any free variables ?

Answer 2

x+y = 2
x-y = 4

may work

Answer 3

the system is consistent as the ranks of coefficient and augmented matrices are equal to 2
is this wat u looki ng for ?

Answer 4

May be!! I am so sorry. I will have test at 10:30 and have only this question not answer yet. Cannot think anything else at this moment. Need help and rely on you only.

Answer 5

I don't know why I am so nervous for this test which never happen before. 30 more minutes and then whatsoever.

Answer 6

ok, you wil do great im sure :)

3 things :-
1)we say a system is consistent if it has unique OR infinitely many solutions.
2)when we get free variables, we will have infinitely many solutions
3)when we dont get any free variables, we will have am uniq solution

Answer 7

Got you. Thanks a lot.

Answer 8

np :) all the best for the test =))

Answer 9

Thank you very much