6 In this question you must show detailed reasoning.
The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { l l } 1 & 2
0 & 1 \end{array} \right)\).
- Define the transformation represented by \(\mathbf { A }\).
- Show that the area of any object shape is invariant under the transformation represented by \(\mathbf { A }\).
The matrix \(\mathbf { B }\) is given by \(\mathbf { B } = \left( \begin{array} { r l } 7 & 2
21 & 7 \end{array} \right)\). You are given that \(\mathbf { B }\) represents the transformation which is the result of applying the following three transformations in the given order.
- A shear which leaves the \(y\)-axis invariant and which transforms the point \(( 1,1 )\) to the point (1, 4).
- The transformation represented by \(\mathbf { A }\).
- A stretch of scale factor \(p\) which leaves the \(x\)-axis invariant.
- Determine the value of \(p\).