Let $M=\langle x_1,x_2,x_3\rangle$ be a set of linearly independent set of vectors in vector space V. Let $N=\langle y_1,y_2,y_3\rangle$, where $y_1=x_1+x_2, y_2=x_1+x_3, y_3=x_2+x_3$. Find if N is linearly dependent or independent.
I figured that I will have to solve this equation and see if $c_n$ have non trivial solutions.
$c_1y_1+c_2y_2+c_3y_3=0 \rightarrow c_1(x_1+x_2)+c_2(x_1+x_3)+c_3(x_2+x_3)=0$
However, I do not how to proceed from here. Any help is much appreciated.