| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2025 |
| Session | February |
| Marks | 5 |
| Topic | Matrices |
| Type | Solving matrix equations for unknown matrix |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths matrix question requiring standard techniques: finding the inverse of a 2×2 matrix (routine formula application) and solving a matrix equation by post-multiplying by the inverse. Both parts are direct applications of basic matrix algebra with no conceptual challenges or problem-solving required, making it slightly easier than average but still requiring correct algebraic manipulation. |
| Spec | 4.03n Inverse 2x2 matrix4.03r Solve simultaneous equations: using inverse matrix |
The matrix $\mathbf{A}$ is given by $\mathbf{A} = \begin{pmatrix} 2 & a \\ 0 & 1 \end{pmatrix}$, where $a$ is a constant.
\begin{enumerate}[label=(\roman*)]
\item Find $\mathbf{A}^{-1}$.
[2]
\end{enumerate}
The matrix $\mathbf{B}$ is given by $\mathbf{B} = \begin{pmatrix} 2 & a \\ 4 & 1 \end{pmatrix}$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Given that $\mathbf{PA} = \mathbf{B}$, find the matrix $\mathbf{P}$.
[3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2025 Q4 [5]}}