Question

Show that the following systems of equations is inconsistent. 

x + y – 2z = 5; 

x – 2y + z = - 2; 

- 2x + y + z = 4.

Answer 1

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

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.