Consider the vector equation c1v1+c2v2=0c_1 v_1 + c_2 v_2 = 0c1v1+c2v2=0 where v1=(12)v_1 = \begin{pmatrix} 1 \\ 2 \end{pmatrix}v1=(12) and v2=(36)v_2 = \begin{pmatrix} 3 \\ 6 \end{pmatrix}v2=(36). What can be concluded?
The vectors are linearly independent.
The only solution is c1=c2=0c_1 = c_2 = 0c1=c2=0.
There exist non-zero scalars c1,c2c_1, c_2c1,c2 satisfying the equation.
The span of these vectors is R2\mathbb{R}^2R2.