Answer :


To prove: Set of given lines are inconsistent.


Given set of lines are : -


x + y – 2z = 5;


x – 2y + z = - 2;


- 2x + y + z = 4


Converting the following equations in matrix form,


AX = B


=


R2 – R1


R3 + 2R1


=


R3 + R2


=


Converting back into equation form we get,


x + y – 2z = 5;


0x – 3y + 3z = - 7;


0x + 0y + 0z = 7


0 = 7


Which is not true.


x + y – 2z = 5;


x – 2y + z = - 2;


- 2x + y + z = 4


are inconsistent.


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