Q. 8

# Show that each one of the following systems of equations is inconsistent.3x – y – 2z = 2;2y – z = - 1;3x – 5y = 3.

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.

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