# How to find a basis of a subspace

1. Jan 25, 2009

### jeffreylze

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

Find bases for the following subspaces of R^3

(a) The set of vectors lying in the plane 2x-y-z=0
(b) The set of vectors on the line x/2=y/3=z/4

2. Relevant equations

3. The attempt at a solution

For part (a) , i tried using this method - X=x , y=y and z = 2x -y , hence (x , y, 2x-y). Then x(1,0,2)+y(0,1,-1) . Hence the basis is {(1,0,2) , (0,1,-1)} But then, i tried put y = 2x-z, x=x and z=z and i found a completely different answer. Why is that so? an x = y/2 + z/2 , y=y and z=z gives a different answer too..

For part (b) , I have absolutely no idea where to start.