Matrix algebra and linear transformationsEdexcel A-Level Further Maths: Mind map

Exam questions on Matrix algebra and linear transformations

1. $\mathbf{A}=\begin{pmatrix}2&1\\0&3\end{pmatrix}$ and $\mathbf{B}=\begin{pmatrix}1&-1\\2&0\end{pmatrix}$.
   Find the matrix $\mathbf{C}$ such that $\mathbf{A}+\mathbf{C}=2\mathbf{B}$.2 marks
2. Transformation $\mathrm{P}$ is a reflection in the line $y=x$. Transformation $\mathrm{Q}$ is a rotation through $90^\circ$ anticlockwise about the origin. The matrix $\mathbf{M}$ represents $\mathrm{P}$ followed by $\mathrm{Q}$.
   Find $\mathbf{M}$ and describe fully the single transformation represented by $\mathbf{M}$.2 marks
3. The matrix $\mathbf{T}$ represents an enlargement with scale factor $3$ and centre the origin, followed by a stretch with scale factor $2$ parallel to the $x$-axis.
   Find $\mathbf{T}$.3 marks