Is a set with a 0 vector linearly independent?

[Sasor]

I don't know how to write out matrices nicely on this forum,

but suppose you have some matrices:[1 0 3]
[2 0 4]
[0 0 5]

This would, by definition, be linearly dependent, spanning a plane in r3..is this correct? Since c1=0, c2=anything, c3=0

where c1v1+c2v2+c3v3=0

With this:

[1 0 3 5]
[3 0 2 4]
[2 0 1 4]

Linearly dependent, spanning all of r3?

[1 4 0 5 2]
[2 3 0 2 4]
[2 9 0 1 1]

Linearly dependent, spanning all of r3?

Are these correct? does the 0 vector have any special properties with this?

 

[micromass]

If a set contains the zero vector, then it is always linearly dependent.

I think you made a typo when writing the title.