# What is the span of {(1; 1; 0),(0; 0; 2)}?

1. Apr 4, 2014

### negation

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

What is the span of {(1; 1; 0),(0; 0; 2)}?

3. The attempt at a solution

So the span is λ1(1; 1; 0) + λ2(0; 0; 2)

But how should I express my answer?
The given answer on the sheet is as below:
The span is {( λ,λ,β )|λ,βεR}

2. Apr 4, 2014

### Staff: Mentor

The span is all linear combinations of <1, 1, 0> and <0, 0, 2>, which is the same span as all linear combinations of <1, 1, 0> and <0, 0, 1>.

Using the same letters as in the answer, the span is all vectors of the form λ<1, 1, 0> + β<0, 0, 1> = <λ, λ, 0> + <0, 0, β>, or more simply, <λ, λ, β>, with λ and β arbitrary reals.

3. Apr 4, 2014

### negation

In red, where did <0,0,1> came from? 2<0,0,1> = <0,0,2>?

Edit: Alright, let's not complicate things since my intention was only to know why the answer was expressed in the way it was.
Thanks

Last edited: Apr 4, 2014
4. Apr 4, 2014

### Staff: Mentor

Yes, <0, 0, 2> is a scalar multiple of <0, 0, 1>. You could just as well have picked <0, 0, 17>.