To prove: Set of given lines are inconsistent.

Given set of lines are : -

3x – y – 2z = 2;

2y – z = - 1;

3x – 5y = 3

Converting the following equations in matrix form,

AX = B

=

R₃ - R₁

=

R₃ + 2R₂

=

Converting back into equation form we get,

3x – y – 2z = 2;

2y – z = - 1;

0x + 0y + 0z = - 1

∴ 0 = - 1

Which is not true.

∴3x – y – 2z = 2;

2y – z = - 1;

3x – 5y = 3

are inconsistent.