Eigenvalues and eigenvectorsEdexcel International A Level Further Maths: Mind map

Exam questions on Eigenvalues and eigenvectors

1. $\mathbf{A}=\begin{pmatrix} 4 & 1 \\ 2 & 3 \end{pmatrix}$.
   Find a normalised eigenvector of $\mathbf{A}$ corresponding to the eigenvalue $2$.2 marks
2. $\mathbf{B}=\begin{pmatrix} 2 & 0 & 0 \\ 0 & 3 & 4 \\ 0 & 4 & 9 \end{pmatrix}$.
   Find an eigenvector of $\mathbf{B}$ corresponding to the eigenvalue $2$.2 marks
3. The matrix $\mathbf{M}=\begin{pmatrix} 5 & k \\ 1 & 2 \end{pmatrix}$, where $k$ is a constant, has $\begin{pmatrix} 2 \\ 1 \end{pmatrix}$ as an eigenvector.
   Find the eigenvalue corresponding to this eigenvector, and the value of $k$.3 marks