AQA
Further Paper 2
Specimen
— Question 12
18 marks
Exam Board
AQA
Module
Further Paper 2 (Further Paper 2)
Session
Specimen
Marks
18
Topic
Invariant lines and eigenvalues and vectors
12
Given that 4 is an eigenvalue of \(\mathbf { M }\), find a corresponding eigenvector. [0pt]
[3 marks]
12
Given that \(\mathbf { M U } = \mathbf { U D }\), where \(\mathbf { D }\) is a diagonal matrix, find possible matrices for \(\mathbf { D }\) and \(\mathbf { U }\). [8 marks]
\(13 \quad \mathbf { S }\) is a singular matrix such that
$$\operatorname { det } \mathbf { S } = \left| \begin{array} { c c c }
a & a & x
x - b & a - b & x + 1
x ^ { 2 } & a ^ { 2 } & a x
\end{array} \right|$$
Express the possible values of \(x\) in terms of \(a\) and \(b\). [0pt]
[7 marks]