# Math Help - Linearly dependency and coplanarity of vectors

1. ## Linearly dependency and coplanarity of vectors

the question is:

is this set of vectors coplanar?
(1,-1,1),(0,1,1),(1,0,2)

I am getting an answer of no because I am finding that a+b+c=0 but only if a=b=c=0
and they that would not make them linearly dependent, thus not coplanar

i did a(1,-1,1)+b(0,1,1+c(1,0,2)=0
I went on to try to solve for each letter always coming up with a=b=c=0

the correct answer should be yes they are coplanar though

2. For example:

$r\begin{bmatrix}{1}&{-1}&{1}\\{0}&{1}&{1}\\{1}&{0}&{2}\end{bmatrix}=2$

So, the rows generate a subspace $W$ such that $\dim W=2$ (plane).

Fernando Revilla