3. (i)
$$\mathbf { A } = \left( \begin{array} { c c }
\frac { 1 } { \sqrt { } 2 } & \frac { - 1 } { \sqrt { } 2 }
\frac { 1 } { \sqrt { } 2 } & \frac { 1 } { \sqrt { } 2 }
\end{array} \right)$$
- Describe fully the single transformation represented by the matrix \(\mathbf { A }\).
The matrix \(\mathbf { B }\) represents an enlargement, scale factor - 2 , with centre the origin.
- Write down the matrix \(\mathbf { B }\).
(ii)
$$\mathbf { M } = \left( \begin{array} { c c }
3 & k
- 2 & 3
\end{array} \right) , \quad \text { where } k \text { is a positive constant. }$$
Triangle \(T\) has an area of 16 square units.
Triangle \(T\) is transformed onto the triangle \(T ^ { \prime }\) by the transformation represented by the matrix M.
Given that the area of the triangle \(T ^ { \prime }\) is 224 square units, find the value of \(k\).