Edexcel FP1 2010 June — Question 6

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJune
TopicLinear transformations

6. Write down the \(2 \times 2\) matrix that represents
  1. an enlargement with centre \(( 0,0 )\) and scale factor 8 ,
  2. a reflection in the \(x\)-axis. Hence, or otherwise,
  3. find the matrix \(\mathbf { T }\) that represents an enlargement with centre ( 0,0 ) and scale factor 8, followed by a reflection in the \(x\)-axis. $$\mathbf { A } = \left( \begin{array} { l l } 6 & 1
    4 & 2 \end{array} \right) \text { and } \mathbf { B } = \left( \begin{array} { r r } k & 1
    c & - 6 \end{array} \right) , \text { where } k \text { and } c \text { are constants. }$$
  4. Find \(\mathbf { A B }\). Given that \(\mathbf { A B }\) represents the same transformation as \(\mathbf { T }\),
  5. find the value of \(k\) and the value of \(c\).