Edexcel F3 2014 June — Question 4

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2014
SessionJune
Topic3x3 Matrices

4. A non-singular matrix \(\mathbf { M }\) is given by $$\mathbf { M } = \left( \begin{array} { l l l } 3 & k & 0
k & 2 & 0
k & 0 & 1 \end{array} \right) \text {, where } k \text { is a constant. }$$
  1. Find, in terms of \(k\), the inverse of the matrix \(\mathbf { M }\). The point \(A\) is mapped onto the point ( \(- 5,10,7\) ) by the transformation represented by the matrix $$\left( \begin{array} { l l l } 3 & 1 & 0
    1 & 2 & 0
    1 & 0 & 1 \end{array} \right)$$
  2. Find the coordinates of the point \(A\).