# Simple question regarding general solutions

1. Feb 11, 2013

### MoreDrinks

1. The problem statement, all variables and given/known data
Solve the homogeneous system of equations.

2. Relevant equations
The relevant matrix is like so:
1 0 0
-1 0 0
3-5 0

3. The attempt at a solution
Add R1 to R2, then add -3R1 to R3.

1 0 0
0 0 0
0-5 0

Interchange R2 and R3, then divide the new R2 by -1/5

1 0 0
0 1 0
0 0 0

Under other circumstances where there's a general solution to such a matrix, with a row of zeroes on the bottom, but not an empty column for x3, you would write x3=r or what have you and then include r when solving for x1 and x2. In this case, where x1 and x2 simply equal zero, what would one write about x3?

Last edited: Feb 11, 2013
2. Feb 11, 2013

### Staff: Mentor

x3 is arbitrary, meaning it can have any value.

3. Feb 11, 2013

### Karnage1993

In this case, you still have to set $x_3 = r$ for some $r \in \mathbb{R}$.

4. Feb 11, 2013

### MoreDrinks

Thank you both.

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