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.