CAIE FP1 2011 June — Question 3

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJune
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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 .
3 The linear transformation $\mathrm { T } : \mathbb { R } ^ { 4 } \rightarrow \mathbb { R } ^ { 4 }$ is represented by the matrix $\mathbf { M } = \left( \begin{array} { r r r r } 1 & 3 & - 2 & 4 \\ 5 & 15 & - 9 & 19 \\ - 2 & - 6 & 3 & - 7 \\ 3 & 9 & - 5 & 11 \end{array} \right)$.\\
(i) Find the rank of $\mathbf { M }$.\\
(ii) Obtain a basis for the null space of T .

\hfill \mbox{\textit{CAIE FP1 2011 Q3}}
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Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 EITHER Q11 OR