Answer :


To prove: Set of given lines are inconsistent.


Given set of lines are : -


x + 2y + 4z = 12;


y + 2z = - 1;


3x + 2y + 4z = 4


Converting the following equations in matrix form,


AX = B


=


R3 - 3R1


=


R3 + 4R2


=


Converting back into equation form we get,


x + 2y + 4z = 12;


y + 2z = - 1;


0x + 0y + 0z = - 36


0 = - 36


Which is not true.


2x – y + 3z = 1;


3x – 2y + 5z = - 4;


5x – 4y + 9z = 14


are inconsistent.


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