Are the vectors $v_{1},v_{2},v_{3}$ linear independant?
$$v_{1}=\begin{pmatrix} &1& \\ &1&\\ &1& \end{pmatrix},v_{2}=\begin{pmatrix} &1& \\ &0&\\ &0& \end{pmatrix},v_{3}= \begin{pmatrix} &0& \\ &1&\\ &1& \end{pmatrix}$$
So I wrote this:
$$a\begin{pmatrix} &1& \\ &1&\\ &1& \end{pmatrix}+b\begin{pmatrix} &1& \\ &0&\\ &0& \end{pmatrix}+c \begin{pmatrix} &0& \\ &1&\\ &1& \end{pmatrix}= \begin{pmatrix} &0& \\ &0&\\ &0& \end{pmatrix}$$
From this we get these linear systems:
$$I: a+b=0$$
$$II: a+c=0$$
$$III: a+c=0$$
But I cannot solve it because II and III is same so actually we only have $2$ systems with $3$ unknowns I don't know what to do...? >.<
you can write $$b=-a$$ and $$c=-a$$ and your vectors are dependant