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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