Question

Show that the following systems of equations is inconsistent. 

2x – y + 3z = 1; 

3x – 2y + 5z = - 4; 

5x – 4y + 9z = 14.

Answer 1

To prove: Set of given lines are inconsistent. 

Given set of lines are : 

- 2x – y + 3z = 1; 

3x – 2y + 5z = - 4; 

5x – 4y + 9z = 14 

Converting the following equations in matrix form, 

AX = B

2R₂ – 3R₁ 

2R₃ - 5R₁

Converting back into equation form we get, 

2x – y + 3z = 1; 

0x – 1y + 1z = - 11; 

0x + 0y + 0z = 56 

∴ 0 = 56 

Which is not true. 

∴2x – y + 3z = 1; 

3x – 2y + 5z = - 4; 

5x – 4y + 9z = 14 

are inconsistent.