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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