Given that \(| x | < 1\), prove that
$$\tanh ^ { - 1 } x = \frac { 1 } { 2 } \ln \left( \frac { 1 + x } { 1 - x } \right)$$
6
Solve the equation
$$20 \operatorname { sech } ^ { 2 } x - 11 \tanh x = 16$$
Give your answer in logarithmic form.
\(7 \quad\) The matrix \(\mathbf { M }\) is defined as
$$\mathbf { M } = \left[ \begin{array} { c c c }
1 & 7 & - 3
3 & 6 & k + 1
1 & 3 & 2
\end{array} \right]$$
where \(k\) is a constant.