Determinants and inverse matricesEdexcel A-Level Further Maths: Mind map

Exam questions on Determinants and inverse matrices

1. 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
2. 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
3. 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