# Homework Help: Matrix over Z7 needs revision please

1. Oct 11, 2011

### JPanthon

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

Solve

-x1 + 6x2 -2x3 = 0
5x1 + x2 + 2x3 = 0

over Z7

Additional Question: How can we immediately tell there is more than one solution?

2. Relevant equations

Don't know.
3. The attempt at a solution

[-1 6 -2 0]_________[ (-1mod7) 6 (-2mod7) 0]
[5 1 2 0] _____=> [____5_____1____2_____0]

=> [1 6 2 0] (-5R1 + R2) => [1_____6__________2_____0]
____[5 1 2 0] ________________[0___-29mod7___-8mod7___0]

=> [1 6 2 0]________(-6R2 + R1) => [1 0 4 0]
____[0 1 1 0]______________________[0 1 1 0]

So the solution set is {(-4x3, -x3, x3) : x3 element of Z7}

How does this look?
Sorry if it's messy! I did my best

2. Oct 11, 2011

### JPanthon

Just realized how ugly it looks!
Sorry, just ignore the underscores and pretend that they are spaces.
Or if you could tell me how to make better matrices on the computer I would be happy to redo my post!

3. Oct 11, 2011

### Staff: Mentor

Post #3 in this LaTeX thread shows a matrix. You can use the "Quote" button on it to see the LaTeX source that was used to make it.