| Exam Board | OCR |
|---|---|
| Module | FP1 AS (Further Pure 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Topic | Matrices |
| Type | Matrix conformability and dimensions |
| Difficulty | Easy -1.3 This is a straightforward question testing basic matrix conformability rules and simple matrix multiplication. Students only need to recall that an m×n matrix can multiply an n×p matrix, identify dimensions (P is 2×3, Q is 1×2), and perform routine multiplication. No problem-solving insight required, just direct application of definitions. |
| Spec | 4.03a Matrix language: terminology and notation4.03b Matrix operations: addition, multiplication, scalar |
1 Matrices $\mathbf { P }$ and $\mathbf { Q }$ are given by $\mathbf { P } = \left( \begin{array} { c c c } 1 & k & 0 \\ - 2 & 1 & 3 \end{array} \right)$ and $\mathbf { Q } = ( ( 1 + k ) - 1 )$ where $k$ is a constant.\\
Exactly one of statements A and B is true.\\
Statement A: $\quad \mathbf { P }$ and $\mathbf { Q }$ (in that order) are conformable for multiplication.\\
Statement B: $\quad \mathbf { Q }$ and $\mathbf { P }$ (in that order) are conformable for multiplication.
\begin{enumerate}[label=(\alph*)]
\item State, with a reason, which one of A and B is true.
\item Find either $\mathbf { P Q }$ or $\mathbf { Q P }$ in terms of $k$.
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 AS 2021 Q1 [4]}}