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Apply the test of rank to examine whethe...

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.

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The system of equations -2x+y+z=a,x-2y+z=b,x+y-2z=c is consistent if

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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 .