Linear Alg: Find all values of a and determine all solutions

[sumtingwong59]

Homework Statement

x - 2y + z = 0
x + ay - 3z = 0
-x + 6y - 5z = 0

Homework Equations

3. The Attempt at a Solution [/B]

i've got it reduced all the way down to
1 0 0 0
0 1 -1 0
0 0 -1a+3 0

I could show more of the steps if needed, but I am just wondering what I can do to reduce the matrix further, or how i could get solutions from what i have so far

 

[O_o]

I think your reduced form is off.

I get

1 0 -1
0 a-2 0
0 1 -1If you want to find the solutions then you need to figure out what this matrix is telling you. Start with rows 1 and 3. What do they tell you about the relationship between x, y and z? If you can figure out those then we can move onto the second row which is slightly different.