AQA
Further Paper 2
2019
June
— Question 9
4 marks
Exam Board
AQA
Module
Further Paper 2 (Further Paper 2)
Year
2019
Session
June
Marks
4
Topic
Invariant lines and eigenvalues and vectors
9
Find the eigenvalues and corresponding eigenvectors of the matrix
$$\mathbf { M } = \left[ \begin{array} { c c }
\frac { 1 } { 5 } & \frac { 2 } { 5 }
\frac { - 3 } { 5 } & \frac { 13 } { 10 }
\end{array} \right]$$
9
Find matrices \(\mathbf { U }\) and \(\mathbf { D }\) such that \(\mathbf { D }\) is a diagonal matrix and \(\mathbf { M } = \mathbf { U D U } ^ { - 1 }\)
9
Given that \(\mathbf { M } ^ { n } \rightarrow \mathbf { L }\) as \(n \rightarrow \infty\), find the matrix \(\mathbf { L }\). [0pt]
[4 marks]
9
The transformation represented by \(\mathbf { L }\) maps all points onto a line. Find the equation of this line.
\begin{center}
\begin{tabular}{ | l | }