Edexcel F3 2024 January — Question 2

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2024
SessionJanuary
Topic3x3 Matrices

2. $$\mathbf { T } = \left( \begin{array} { l l l } 2 & 3 & 7
3 & 2 & 6
a & 4 & b \end{array} \right) \quad \mathbf { U } = \left( \begin{array} { r r r } 6 & - 1 & - 4
15 & c & - 9
- 8 & a & 5 \end{array} \right)$$ where \(a\), \(b\) and \(c\) are constants.
Given that \(\mathbf { T U } = \mathbf { I }\)
  1. determine the value of \(a\), the value of \(b\) and the value of \(c\) The transformation represented by the matrix \(\mathbf { T }\) transforms the line \(l _ { 1 }\) to the line \(l _ { 2 }\) Given that \(l _ { 2 }\) has equation $$\frac { x - 1 } { 3 } = \frac { y } { - 4 } = z + 2$$
  2. determine a Cartesian equation for \(l _ { 1 }\)