Vector space/Chain/Flag/1/Exercise

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

$V_{0}=0,\,V_{1}=\mathbb {R} {\begin{pmatrix}2\\7\\-5\end{pmatrix}},\,V_{2}=\langle {\begin{pmatrix}4\\-3\\9\end{pmatrix}},{\begin{pmatrix}-6\\-4\\4\end{pmatrix}}\rangle ,\,V_{3}=\mathbb {R} ^{3}.$

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