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fsm
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Homework Statement
Find the basis of the solution space of the homogeneous system of linear equations.
x-2y+3z=0
-3x+6y-9z=0
Homework Equations
Ax=0
The Attempt at a Solution
I first set up my equation
[tex]\left[ \begin{array}{cccc} 1 & 2 & -3 \\ -3 & 6 & 9 \end{array} \right][/tex]*[tex]\left[ \begin{array}{cccc} x \\ y \\ z \end{array} \right][/tex]=0
Then I put A in rref to get:
[tex]\left[ \begin{array}{cccc} 1 & -2 & 0 \\ 0 & 0 & 1 \end{array} \right][/tex]
So I get the system:
x-2y=0
z=0
From here I'm lost. I don't know if I should paramterize or what. I did try setting z=t x=s, but the vectors I got were not correct. Any help would be great.