Showing Linear Dependence My task is to show that the set of vectors:  $\bf x_1, x_2, x_3, x_4$ where
$\bf x_1=[1,0,0]$
$\bf x_2=[t,1,1]$
$\bf x_3=[1,t,t^2]$ and
$\bf x_4=[t+2,t+1,t^2+1]$ are linearly dependent. (Note: $x_i$ can also be written in matrix format.)
To show that they are linearly dependent I form the equation:
$\bf c_1x_1+c_2x_2+c_3x_3+c_4x_4=0$ and will show that there is a nonzero solution to it. That is I will show that aside from $\bf c_1,c_2,c_3,c_4=0$ there is some other solution to it.
However solving puts me in a system of 3 equations in 4 unknowns which seems new to me. They are:
$\bf c_1+c_2t+c_3+c_4(t+2)=0$
$\bf 0+c_2+c_3t+c_4(t+1)=0$ 
$\bf 0+c_2+c_3t^2+c_4(t^2+1)=0$
Can someone help me to find a non trivial solution to the given system of equation? or Will you help me showing that the 4 vectors above are linearly dependent?
Thank you so much for your help. 

Note that $$\bf x_4=x_1+x_2+x_3 \Rightarrow -x_1-x_2-x_3+x_4=0$$
so $\bf c_1=c_2=c_3=-1$ and $\bf c_4=+1$ 
