| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | February |
| Marks | 4 |
| Topic | Matrices |
| Type | Matrix arithmetic operations |
| Difficulty | Easy -1.3 This is a straightforward matrix arithmetic question requiring only basic operations (scalar multiplication and matrix addition/subtraction) with 2×2 matrices. Both parts are routine calculations with no problem-solving or conceptual depth—part (i) is direct computation, and part (ii) simply verifies an identity by subtraction. This is easier than average A-level content, similar to early exercises in a Further Maths matrices chapter. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar |
The matrices $\mathbf{A}$ and $\mathbf{B}$ are given by $\mathbf{A} = \begin{pmatrix} 4 & 1 \\ 0 & 2 \end{pmatrix}$ and $\mathbf{B} = \begin{pmatrix} 1 & 1 \\ 0 & -1 \end{pmatrix}$.
\begin{enumerate}[label=(\roman*)]
\item Find $\mathbf{A} + 3\mathbf{B}$. [2]
\item Show that $\mathbf{A} - \mathbf{B} = k\mathbf{I}$, where $\mathbf{I}$ is the identity matrix and $k$ is a constant whose value should be stated. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2022 Q1 [4]}}