Determine whether or not the following sets $S$ of $2\times 2$ matrices are linearly independent.

Select an Answer Linearly Independent Linearly Dependent  1. $S= \left\{ \begin{pmatrix} -3&1\cr -5&4 \end{pmatrix},\, \begin{pmatrix} 6&-2\cr 10&-8 \end{pmatrix} \right\}$

Select an Answer Linearly Independent Linearly Dependent  2. $S= \left\{ \begin{pmatrix} -3&1\cr -5&4 \end{pmatrix},\, \begin{pmatrix} 6&8\cr 12&-8 \end{pmatrix} \right\}$

Select an Answer Linearly Independent Linearly Dependent  3. $S= \left\{ \begin{pmatrix} -3&1\cr -5&4 \end{pmatrix}, \, \begin{pmatrix} 6&8\cr 12&-8 \end{pmatrix} ,\, \begin{pmatrix} 1&-3\cr 9&10 \end{pmatrix} ,\,\right.$ $\left. \begin{pmatrix} 1&-3\cr -2&-2 \end{pmatrix} ,\, \begin{pmatrix} 17&-31\cr \pi & e^2 \end{pmatrix} \right\}$

Select an Answer Linearly Independent Linearly Dependent  4. $S= \left\{ \begin{pmatrix} 1&-2\cr 2&1 \end{pmatrix},\, \begin{pmatrix} -2&1\cr 1&2 \end{pmatrix},\, \begin{pmatrix} -2&2\cr 1&0 \end{pmatrix} \right\}$