# Basis question

1. Mar 20, 2013

### kwal0203

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

Find bases for the following subspace a of r^3

Y+z=0

3. The attempt at a solution

First I found a normal to this plane n=(0,1,1)

Then I found two vectors which are orthogonal to the normal u=(0,-1,1), v=(1,0,0)

Is this correct the answer in my book has v=(7,0,0)

Thanks

2. Mar 20, 2013

### HallsofIvy

You are correct. If that is what your book really says it is wrong. Any vector in $$R^3$$ is of the form (x, y, z). Any vector for which z= -y is of the form (x, y, -y)= (x, 0, 0)+ (0, y, -y)= x(1, 0, 0)+ y(0, 1, -1). Of course, (7, 0, 0) would work as well as (1, 0, 0) but this subspace is definitely two dimensional.

3. Mar 20, 2013

### kwal0203

Great thanks for that. I can see why x=7 works it just confused me why they put that as the only answer @.@