| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2023 |
| Session | January |
| Marks | 5 |
| Topic | Matrices |
| Type | Matrix arithmetic operations |
| Difficulty | Easy -1.3 This is a straightforward matrix arithmetic question requiring only basic operations (addition, scalar multiplication, matrix multiplication). Part (i) involves simple element-wise calculations with no conceptual challenge, and part (ii) is routine 2×2 matrix multiplication. Both are direct applications of definitions with no problem-solving or insight required, making this easier than average. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar |
The matrices $\mathbf{A}$ and $\mathbf{B}$ are given by $\mathbf{A} = \begin{pmatrix} 2 & a \\ 0 & 1 \end{pmatrix}$ and $\mathbf{B} = \begin{pmatrix} 2 & a \\ 4 & 1 \end{pmatrix}$. $\mathbf{I}$ denotes the $2 \times 2$ identity matrix.
Find
\begin{enumerate}[label=(\roman*)]
\item $\mathbf{A} + 3\mathbf{B} - 4\mathbf{I}$. [3]
\item $\mathbf{AB}$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2023 Q1 [5]}}