Consider the vectors,
\(v_1 = \begin{pmatrix} 1 \\ 7 \\ -4 \end{pmatrix}, v_2 = \begin{pmatrix} -4 \\ -1 \\ 4 \end{pmatrix}, v_3 = \begin{pmatrix} r \\ 17 \\ -20 \end{pmatrix}\).
a. For which value(s) of \(r\) are the vectors linearly independent?
b. For which value(s) of \(r\) is \(v_3 \in \text{Span}\{v_1, v_2\}\)?
If there is more than one value, use interval notation (e.g., \(x \le -1\) or \(x > 2\) is written \((-\infty, -1] \cup (2, +\infty)\)).
