Matrix algebra

Sample questions

Original practice questions written in the style of the exam.

1. Question 15 marks

   $\mathbf{A} = \begin{pmatrix} k & 3 \\ 2 & k - 1 \end{pmatrix}$ where $k$ is a constant.

   (a) Find the values of $k$ for which $\mathbf{A}$ is singular.

   (b) Given that $k = 1$, find $\mathbf{A}^{-1}$.

   Mark scheme

   • M1 $\det \mathbf{A} = k(k - 1) - 6$ set equal to $0$ (1)
   • M1 $k^2-k-6=0\Rightarrow (k-3)$ (1)