Invariant points and linesEdexcel A-Level Further Maths: Mind map

Exam questions on Invariant points and lines

1. The matrix $\mathbf{A}=\begin{pmatrix}3&-2\\ 1&0\end{pmatrix}$ represents a linear transformation of the plane.
   Find the coordinates of all the invariant points of the transformation.2 marks
2. The matrix $\mathbf{M}=\begin{pmatrix}2&0\\ 0&3\end{pmatrix}$ represents a linear transformation of the plane.
   Find the equations of all the invariant lines through the origin.2 marks
3. The matrix $\mathbf{B}=\begin{pmatrix}4&2\\ 1&3\end{pmatrix}$ represents a linear transformation of the plane.
   Show that the invariant lines through the origin of the form $y=mx$ satisfy $2m^2+m-1=0$.3 marks