Apply the test of rank to examine whether the equations `x+y+z=6,x-y+z=2,2x-y+3z=9` is consistent or inconsistent and if consistent find the complete solution.

Examine the consistency of the following systems of equations x+y+z=1,2x+y+z=2,x+2y+2z=1 and if consistent find the complete solutions.

Examine whether the following system of equations are consistent or inconsistent and if consistent, find the complete solution, x+y+z = 1, 2x+y+z = 2, x+2y+2z = 1 .

Examine the consistency of the following systems of equations x+y+z=6,x+2y+3z=10,x+2y+4z=1 and if consistent find the complete solutions.

Examine the consistency of the following systems of equations x+y+z=9,2x+5y+7z=52,2x+y-z=0 and if consistent find the complete solutions.