inland reef
I need some assistance with linear independence and basis in a vector space. The vectors $v_1, v_2, v_3, v_4, v_5$ are given in the plane as shown in the figure below. I'm trying to determine which of the following statements are true:
\begin{enumerate}
\item The set $\left{ v_3, v_4, v_1\right}$ is linearly dependent.
\item The set $\left{ v_1, v_4\right}$ is linearly dependent.
\item The set $\left{ v_1, v_2\right}$ is linearly dependent.
\item The set $\left{ v_4, v_2, v_5\right}$ is linearly independent.
\item The set $\left{ v_3, v_4, v_1\right}$ forms a basis in the plane.
\item The set $\left{ v_3, v_4\right}$ forms a basis in the plane.
\item The set $\left{ v_5, v_1\right}$ is linearly independent.
\item The set $\left{ v_3, v_4\right}$ forms a basis in the space.
\item The set $\left{ v_1, v_2\right}$ is linearly independent.
\item The set $\left{ v_4, v_2, v_5\right}$ forms a basis in the space.
\end{enumerate}
Please mark all the true statements.
mossy meteor