Linear transformationsAQA A-Level Further Maths: Mind map

Exam questions on Linear transformations

1. The matrix $\mathbf{M}=\begin{pmatrix}0&-1\\1&0\end{pmatrix}$ represents a transformation $T$ of the plane.
   The point $P$ is mapped by $T$ to $(-4,5)$. Find the coordinates of $P$.2 marks
2. The unit square $OABC$ has vertices $O(0,0)$, $A(1,0)$, $B(1,1)$ and $C(0,1)$. It is transformed by the matrix $\mathbf{N}=\begin{pmatrix}1&2\\0&1\end{pmatrix}$.
   Describe fully the single transformation represented by $\mathbf{N}^2$.2 marks
3. Transformation $P$ is a rotation through $90^\circ$ clockwise about the origin, and transformation $Q$ is a reflection in the line $y=x$.
   Find the single matrix that represents $P$ followed by $Q$.3 marks