Q. 6

# Show that each one of the following systems of equations is inconsistent.2x – y + 3z = 1;3x – 2y + 5z = - 4;5x – 4y + 9z = 14.

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 = R3 - 3R2 = 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.

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