Question

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) $q_1 = \begin{bmatrix} 1\\1\\-1\\0 \end{bmatrix}$, $q_2 = \begin{bmatrix} 0\\1\\-1\\1 \end{bmatrix}$, $q_3 = \begin{bmatrix} -1\\0\\0\\-1 \end{bmatrix}$.

          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) $q_1 = \begin{bmatrix} 1\\1\\-1\\0 \end{bmatrix}$, $q_2 = \begin{bmatrix} 0\\1\\-1\\1 \end{bmatrix}$, $q_3 = \begin{bmatrix} -1\\0\\0\\-1 \end{bmatrix}$.

Are the following vector set {q1, q2, q3} linearly independent?
a) q1 =
< b m a t r i x >, q2 =
< b m a t r i x >, q3 =
< b m a t r i x >;
b) q1 =
< b m a t r i x >, q2 =
< b m a t r i x >, q3 =
< b m a t r i x >;
c) q1 =
< b m a t r i x >, q2 =
< b m a t r i x >, q3 =
< b m a t r i x >.

Added by Alexis L.

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