| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 5 |
| Topic | Matrices |
| Type | Matrix inverse calculation |
| Difficulty | Moderate -0.8 Part (a) is a routine matrix inversion using the standard 2×2 formula. Part (b) requires knowing that det(A²) = (det A)² and solving a simple quadratic equation. Both parts are straightforward applications of standard Further Maths techniques with no problem-solving insight required, making this easier than average. |
| Spec | 4.03h Determinant 2x2: calculation4.03m det(AB) = det(A)*det(B)4.03n Inverse 2x2 matrix |
$$\mathbf{A} = \begin{bmatrix} 2 & 3 \\ k & 1 \end{bmatrix}$$
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf{A}^{-1}$ [2 marks]
\item The determinant of $\mathbf{A}^2$ is equal to 4.
Find the possible values of $k$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q1 [5]}}