Show that the matrix \(\left[ \begin{array} { c c } 5 - k & 2 k ^ { 3 } + 1 & k \end{array} \right]\) is singular when \(k = 1\).
12
Find the values of \(k\) for which the matrix \(\left[ \begin{array} { c c } 5 - k & 2 k ^ { 3 } + 1 & k \end{array} \right]\) has a negative determinant. Fully justify your answer.
\(13 \frac { \text { The graph of the rational function } y = \mathrm { f } ( x ) \text { intersects the } x \text {-axis exactly once at } } { ( - 3,0 ) }\)
The graph has exactly two asymptotes, \(y = 2\) and \(x = - 1\)