# Interesting Linear Algebra Problem

1. Aug 31, 2009

### Newtime

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

Let x=(1,0,0) y=(2,1,0) and z=(2,2,1) be column vectors in R3. Consider the set V={tx+sy+uz 0$$\leq$$t,s,u$$\leq$$1}. What does this look like specifically?

2. Relevant equations

n/a

3. The attempt at a solution

No work here, just a thinking problem, but I thought that the set V would fill the solid (a paralellapipid?) formed by the three vectors x,y, and z. Is this correct? Other than visualization, I suppose a reason for this would be that it is analagous to a similar problem in R2 in which the set vills the parallelogram formed by the two vectors. Thanks.

Last edited: Aug 31, 2009
2. Aug 31, 2009

### Staff: Mentor

If the given vectors were linearly independent, set V would be a three-D region in space, but if they are linearly dependent V will be only a one- or two-dimensional subset of R3.

3. Aug 31, 2009

### Newtime

They are linearly independent. And I know they fill some space in R3 but the question was which space...as in to describe it. So my best explanation is the vectors fill the paralellepiped formed by the three vectors. Isn't this correct?

4. Aug 31, 2009

### Dick

Yes, you are visualizing it correctly.

5. Aug 31, 2009

### Newtime

Thanks, I figured I was but wanted to check with all the gurus here.