(Solved): 4. Determine if the set of vectors below are linearly independent/dependent. Use appropriate work/ ...

4. Determine if the set of vectors below are linearly independent/dependent. Use appropriate work/theorems discussed in class to justify your answer. (a) \[ \left\{\left[\begin{array}{l} 1 \\ 2 \end{array}\right],\left[\begin{array}{l} -3 \\ -\pi \end{array}\right],\left[\begin{array}{l} 74 \\ e^{2} \end{array}\right]\right\} \] (b) \[ \left\{\left[\begin{array}{l} 1 \\ 2 \\ 3 \end{array}\right],\left[\begin{array}{l} 4 \\ 5 \\ 6 \end{array}\right],\left[\begin{array}{l} 7 \\ 8 \\ 9 \end{array}\right]\right\} \] (c) \[ \left\{\left[\begin{array}{l} 1 \\ 0 \\ 0 \\ 1 \end{array}\right],\left[\begin{array}{l} 0 \\ 1 \\ 1 \\ 0 \end{array}\right],\left[\begin{array}{c} 1 \\ 0 \\ -1 \\ 0 \end{array}\right]\right\} \] (d) \[ \left\{\left[\begin{array}{c} -12 \\ 0 \\ 16 \\ 2 \\ -6 \end{array}\right],\left[\begin{array}{l} 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{array}\right],\left[\begin{array}{l} 0 \\ 0 \\ 2 \\ 3 \\ 0 \end{array}\right]\left[\begin{array}{c} 6 \\ 0 \\ -8 \\ -1 \\ 3 \end{array}\right]\left[\begin{array}{c} 1 \\ -1 \\ 1 \\ -1 \\ 1 \end{array}\right]\right\} \]