Q. 5

# 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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