CAIE FP1 2011 June — Question 3

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJune
Topic3x3 Matrices

3 The linear transformation \(\mathrm { T } : \mathbb { R } ^ { 4 } \rightarrow \mathbb { R } ^ { 4 }\) is represented by the matrix \(\mathbf { M } = \left( \begin{array} { r r r r } 1 & 3 & - 2 & 4
5 & 15 & - 9 & 19
- 2 & - 6 & 3 & - 7
3 & 9 & - 5 & 11 \end{array} \right)\).
  1. Find the rank of \(\mathbf { M }\).
  2. Obtain a basis for the null space of T .