- #1
JPanthon
- 20
- 0
Homework Statement
Solve
-x1 + 6x2 -2x3 = 0
5x1 + x2 + 2x3 = 0
over Z7
Additional Question: How can we immediately tell there is more than one solution?
Homework Equations
Don't know.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