Question

Determine whether the given set is a basis for the given plane or hyperplane

Answer 1

\[\beta=\left\{ \left[\begin{matrix} 1\\1\\0\\1\end{matrix}\right],
\left[\begin{matrix} 1\\-1\\1\\0\end{matrix}\right],
\left[\begin{matrix} 0\\0\\1\\0\end{matrix}\right]\right\}\] for \[2x_1+3x_2-5x_4=0\]