Are the following vector set \{q_1, q_2, q_3\} linearly independent?
a) $q_1 = \begin{bmatrix} -1\\1 \end{bmatrix}$, $q_2 = \begin{bmatrix} 0\\1 \end{bmatrix}$, $q_3 = \begin{bmatrix} 1\\-2 \end{bmatrix}$;
b) $q_1 = \begin{bmatrix} 0\\0\\-2 \end{bmatrix}$, $q_2 = \begin{bmatrix} 1\\-1\\0 \end{bmatrix}$, $q_3 = \begin{bmatrix} 1\\0\\2 \end{bmatrix}$;
c) $q_1 = \begin{bmatrix} 1\\1\\-1\\0 \end{bmatrix}$, $q_2 = \begin{bmatrix} 0\\1\\-1\\1 \end{bmatrix}$, $q_3 = \begin{bmatrix} -1\\0\\0\\-1 \end{bmatrix}$.
