6.
$$\mathbf { M } = \left( \begin{array} { r r }
8 & - 1
- 4 & 2
\end{array} \right)$$
- Find the value of \(\operatorname { det } \mathbf { M }\)
The triangle \(T\) has vertices at the points \(( 4,1 ) , ( 6 , k )\) and \(( 12,1 )\), where \(k\) is a constant.
The triangle \(T\) is transformed onto the triangle \(T ^ { \prime }\) by the transformation represented by the matrix \(\mathbf { M }\).
Given that the area of triangle \(T ^ { \prime }\) is 216 square units, - find the possible values of \(k\).