OCR FP1 2012 January — Question 9

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJanuary
Topic3x3 Matrices

\(\mathbf { 9 }\) The matrix \(\mathbf { X }\) is given by \(\mathbf { X } = \left( \begin{array} { r r r } a & 2 & 9
2 & a & 3
1 & 0 & - 1 \end{array} \right)\).
  1. Find the determinant of \(\mathbf { X }\) in terms of \(a\).
  2. Hence find the values of \(a\) for which \(\mathbf { X }\) is singular.
  3. Given that \(\mathbf { X }\) is non-singular, find \(\mathbf { X } ^ { - 1 }\) in terms of \(a\).