Determinants and inverse matricesEdexcel A-Level Further Maths: Flashcards

What these 13 flashcards ask

Determinant of \begin{pmatrix}a&b\\ c&d\end{pmatrix}?
What does |\det\mathbf{A}| represent for a 2-D transformation?
What does a negative determinant tell you?
What does |\det\mathbf{A}| represent for a 3-D transformation?
When is a matrix singular?
State the inverse of \begin{pmatrix}a&b\\ c&d\end{pmatrix}.
What is (\mathbf{AB})^{-1}?
What is \det(\mathbf{AB})?
What is \det\mathbf{A}^{-1}?
Sign pattern for 3 x 3 cofactors?
Steps to find a 3 x 3 inverse?
What does a singular transformation do to the plane?
If \mathbf{P}\mathbf{x}=\mathbf{y}, how do you find \mathbf{x}?

Exam questions on Determinants and inverse matrices

The matrix $\mathbf{A}=\begin{pmatrix}4&3\\ 2&5\end{pmatrix}$ represents a linear transformation of the plane.
A triangle of area $5$ cm $^2$ is transformed by $\mathbf{A}$ . Find the area of its image, and state whether the orientation of the triangle is preserved.2 marks
The matrix $\mathbf{B}=\begin{pmatrix}k&3\\ 4&k+1\end{pmatrix}$ , where $k$ is a constant.
Given that $k=2$ , find $\mathbf{B}^{-1}$ .2 marks
The matrix $\mathbf{C}=\begin{pmatrix}2&0&1\\ 1&3&-1\\ 0&2&4\end{pmatrix}$ represents a linear transformation of three-dimensional space.
Find $\det\mathbf{C}$ .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).