# Homework Help: Finding System Solutions of the system Ax=0; A being a matrix

1. Jan 28, 2010

### gpax42

1. The problem statement, all variables and given/known data

Find all solutions of the system Ax=0
where A = the 3x3 matrix

[1 3 2]
[2 6 9]
[2 8 8]

2. Relevant equations

not really sure what equations to include

3. The attempt at a solution

wasnt positive how to go about answering this question because im not sure what its asking for...

i turned "x" into a 3x1 matrix consisting of x1, x2 and x3 and tried to solve the system of equations...

1x1 + 3x2 + 2x3 = 0
2x1 + 6x2 + 9x3 = 0
2x1 + 8x2 + 9x3 = 0

after trying to solve this as a linear system of equations problem, i ended getting that each value (x1, x2, x3) was equal to 0... is this anywhere close to a correct approach to this problem? Thanks for any help you have to offer

2. Jan 28, 2010

### rochfor1

Yes, since this matrix is indeed invertible.

3. Jan 28, 2010

### Staff: Mentor

Do you know about row operations for reducing a matrix? If you do, using them to reduce your matrix would be simpler than solving three equations in three unknowns.

4. Jan 28, 2010

### gpax42

My class learned about row operations today but I didn't think to apply them because I began this problem yesterday...

5. Jan 29, 2010

### HallsofIvy

If A is invertible, then the only solution to Ax= 0 is x= 0.

6. Jan 29, 2010