Linear transformations as matricesEdexcel International A Level Further Maths: Mind map

Exam questions on Linear transformations as matrices

1. A linear transformation $T$ of the plane maps $(1,0)$ to $(2,3)$ and $(0,1)$ to $(-1,4)$.
   Find the image of the point $(-2,5)$ under $T$.2 marks
2. The matrix $\mathbf{R}=\begin{pmatrix}0&-1\\ 1&0\end{pmatrix}$ represents the transformation $R$ and the matrix $\mathbf{S}=\begin{pmatrix}1&0\\ 0&-1\end{pmatrix}$ represents the transformation $S$.
   Find the image of the point $(4,1)$ under $S$ followed by $R$.2 marks
3. The linear transformation $T$ is represented by $\mathbf{T}=\begin{pmatrix}2&1\\ -1&3\end{pmatrix}$ and the linear transformation $U$ is represented by $\mathbf{U}=\begin{pmatrix}1&2\\ 0&-1\end{pmatrix}$.
   Find the matrix that represents $T$ followed by $U$, and use it to find the image of the point $(1,2)$ under this combined transformation.3 marks