1. ## Span help

This is NOT for a graded paper, as my other thread was closed. I have a test on Friday, and I'm trying to understand spans. I just attached it because I thought it would be better formatted.

Here are the typed questions instead:

Show that the vectors (1,2-1),(3,1,1),(1,1,0),(1,-3,3) are linearly dependent by writing the zero vector as a nontrivial linear combination of them.

When is the vector (x,y,z) in the span of {(1,2-1),(3,1,1)(1,-3,3)}?

Hope that's better, as I still need some help.

Thanks

2. Originally Posted by shibble
This is NOT for a graded paper, as my other thread was closed. I have a test on Friday, and I'm trying to understand spans. I just attached it because I thought it would be better formatted.

Here are the typed questions instead:

Show that the vectors (1,2-1),(3,1,1),(1,1,0),(1,-3,3) are linearly dependent by writing the zero vector as a nontrivial linear combination of them.

When is the vector (x,y,z) in the span of {(1,2-1),(3,1,1)(1,-3,3)}?
If and only if there are scalars a,b,c such that (x,y,z)=a*(1,2,-1)+b*(3,1,1)+c*(1,-3,3). Hence just solve this system of linear equations for the unknowns a,b,c for (x,y,z)=(0,0,0).

3. Originally Posted by Failure
If and only if there are scalars a,b,c such that (x,y,z)=a*(1,2,-1)+b*(3,1,1)+c*(1,-3,3). Hence just solve this system of linear equations for the unknowns a,b,c for (x,y,z)=(0,0,0).
Is that just for the second part or the first part as well?
For example, for the first one would I just do
a 3b c d 0
2a b c -3d 0
-a b -3d 0

and just solve for this?

4. Originally Posted by shibble
Is that just for the second part or the first part as well?
For example, for the first one would I just do
a 3b c d 0
2a b c -3d 0
-a b -3d 0

and just solve for this?
That's for the first question. And I hope you understand that there always exists the so called trivial solution, that is a=b=c=0. The given vectors are linearly-dependent if and only if there also exist non-trivial solutions of this system of linear equations.