Vector space/Chain/Flag/2/Exercise

Determine whether the following chain of linear subspaces in ${ℝ}^3$ is a flag.

$V_0=0,V_1=ℝ\left(\begin{array}{c}8\\ -3\\ 1\end{array}\right),$

$V_2=\mathrm{kern}\phi ,\text{ where }\phi :{ℝ}^3\to ℝ\text{ is given by the matrix}(1,2,-2),V_3={ℝ}^3.$

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