Show that each one of the following systems of equations is inconsistent.
x + y – 2z = 5;
x – 2y + z = - 2;
- 2x + y + z = 4.
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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