# Math Help - Simple question regarding linear equation ?

1. ## Simple question regarding linear equation ?

Find the value a for which the following system of linear equations has no solution. Solve the system when a = 1.

x1 + 2x2 + 3x3 = 13
-2x1 + x2 - x3 = 4
3x1 + ax3 = -1

I am able to do the following. Solve the system when a = 1. The answer i got is x1 = -1, x2 = 4, x3 = 2. which is correct

But i am not sure on how to do this ? Find the value a for which the following system of linear equations has no solution.

Any help provided will be greatly appericiated.

2. Originally Posted by tester85
Find the value a for which the following system of linear equations has no solution. Solve the system when a = 1.

x1 + 2x2 + 3x3 = 13 .... (1)
-2x1 + x2 - x3 = 4 .... (2)
3x1 + ax3 = -1 .... (3)

I am able to do the following. Solve the system when a = 1. The answer i got is x1 = -1, x2 = 4, x3 = 2. which is correct

But i am not sure on how to do this ? Find the value a for which the following system of linear equations has no solution.

Any help provided will be greatly appericiated.
There are many approaches.

A simple one is to note that if you take equation (1) - 2 x equation (2) and simplify you get:

$x_1 + x_3 = 1 \Rightarrow 3 x_1 + 3 x_3 = 3$.

Clearly this will be inconsistent with equation (3) if a = 3.

3. Great i get it now thanks a lot.