Question 9 - A-Level Maths

Write down the matrix, \(\mathbf { A }\), that represents an enlargement, centre ( 0,0 ), with scale factor \(\sqrt { 2 }\).
The matrix \(\mathbf { B }\) is given by \(\mathbf { B } = \left( \begin{array} { r r } \frac { 1 } { 2 } \sqrt { 2 } & \frac { 1 } { 2 } \sqrt { 2 }
- \frac { 1 } { 2 } \sqrt { 2 } & \frac { 1 } { 2 } \sqrt { 2 } \end{array} \right)\). Describe fully the geometrical transformation represented by \(\mathbf { B }\).
Given that \(\mathbf { C } = \mathbf { A B }\), show that \(\mathbf { C } = \left( \begin{array} { r r } 1 & 1
- 1 & 1 \end{array} \right)\).
Draw a diagram showing the unit square and its image under the transformation represented by \(\mathbf { C }\).
Write down the determinant of \(\mathbf { C }\) and explain briefly how this value relates to the transformation represented by \(\mathbf { C }\).