$$\mathbf { A } = \left( \begin{array} { c c }
- 4 & 10
- 3 & k
\end{array} \right) , \quad \text { where } k \text { is a constant. }$$
The triangle \(T\) is transformed to the triangle \(T ^ { \prime }\) by the transformation represented by \(\mathbf { A }\).
Given that the area of triangle \(T ^ { \prime }\) is twice the area of triangle \(T\), find the possible values of \(k\).
Given that
$$\mathbf { B } = \left( \begin{array} { r r r }
1 & - 2 & 3
- 2 & 5 & 1
\end{array} \right) , \quad \mathbf { C } = \left( \begin{array} { r r }
2 & 8
0 & 2
1 & - 2
\end{array} \right)$$
find \(\mathbf { B C }\).
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