(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the basis of the solution space of the homogeneous system of linear equations.

x-2y+3z=0

-3x+6y-9z=0

2. Relevant equations

Ax=0

3. 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.

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# Homework Help: Basis/Solution set/linear algebra

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