If we apply different elementary row transformation so does the unique solution vary ?

Question

If the rank of a matrix is equal to the rank of augmented matrix then we get a unique solution , Now my ques is that I applied a different row transformation and got the values to be x=7/3 , y=-1/3 and z=7 for a set of equations :

x+y+z=9 , 2x+5y+7z=52 , 2x+y-z=0

But some other answer is given for this ques so that means they must have applied some other row transformation so how can it be unique ?

Answer 1

Yes , You can apply Different row or column transformation on a given equations, but this will not effect the answer .

Your answer seems incorrect as it is not satisfying equation-2 and equation-3.

--> Solving by equation not by row transformation .

 From equation-3 we get  -->    z = 2x + y --(3')           (putting this value in equation-1 and 2  we get).

 -->  3x + 2y = 9 --(1')   &   16x + 12y = 52  --(2')

(Multiplying equation-1' by 6 and then subracting it with equation-2').

We get --> x = 1  & y = 3  (putting these values in equation 3')

     Answer --> x = 1 , y = 3 , z = 5 .