Combined and inverse transformationsEdexcel International A Level Further Maths: Flashcards

What these 13 flashcards ask

Which matrix represents '\mathbf{A} followed by \mathbf{B}'?
Is matrix multiplication commutative?
Inverse of \begin{pmatrix} a & b \\ c & d \end{pmatrix}?
When does \mathbf{M}^{-1} not exist?
What does \mathbf{M}^{-1} do geometrically?
What is (\mathbf{BA})^{-1}?
Area scale factor of a transformation?
What does a negative determinant tell you?
What does \det\mathbf{M}=0 mean geometrically?
Inverse of rotation through \theta anticlockwise about O?
Inverse of reflection in a line?
Inverse of a stretch of factor k or enlargement of factor k?
Area scale factor of \mathbf{A} followed by \mathbf{B}?

Exam questions on Combined and inverse transformations

The matrix $\mathbf{P}=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ represents a rotation through $90^\circ$ anticlockwise about $O$ , and the matrix $\mathbf{Q}=\begin{pmatrix} 2 & 0 \\ 0 & 1 \end{pmatrix}$ represents a stretch parallel to the $x$ -axis with scale factor $2$ .
Find the single matrix that represents $\mathbf{Q}$ followed by $\mathbf{P}$ .2 marks
The matrix $\mathbf{M}=\begin{pmatrix} 4 & 3 \\ 2 & 2 \end{pmatrix}$ represents a transformation of the plane.
A region of area $7\text{ cm}^2$ is transformed by $\mathbf{M}$ . Find the area of its image.2 marks
A triangle $T$ has vertices $O(0,0)$ , $A(2,0)$ and $B(0,3)$ . The matrix $\mathbf{N}=\begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix}$ represents a transformation of the plane, and $T$ is mapped onto triangle $T'$ .
Find the coordinates of $A'$ and $B'$ , the images of $A$ and $B$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).