span of vectors

physicsss

I'm stuck on the following problem:

Describe the span of the vectors u1 and u2 in R^3, where
u1 = (1, 1, 1), u2 = (1, −1, 1)

I know that the span is a(u1)+b(u2), which becomes (a+b,a-b,a+b), but I don't know where to go from here.

TIA.

mathwonk

do you know gaussian elimination, reduction for matrices?

i.e. how to solve for all vectors perpendicular to both of those?

or you could just look at your general vector, since it satisfies an obvious equation.

lurflurf

Consider (1/2)(u1-u2)=(0,1,0) and (1/2)(u1+u2)=(1,0,1)
It will then be easier to see what is happening.

physicsss

Is it the x-z plane in R^3?

mathwonk

have you noticed that the first and third entries of your vectors are equal? what does that tell you about an equations characterizing these vectors?

physicsss

The main diagonal line in x-z plane

mathwonk

i.e. x=z describes all of these vectors.