OCR FP1 AS 2021 June — Question 1 4 marks

Exam BoardOCR
ModuleFP1 AS (Further Pure 1 AS)
Year2021
SessionJune
Marks4
TopicMatrices
TypeMatrix conformability and dimensions
DifficultyEasy -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.
Spec4.03a 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.
  1. State, with a reason, which one of A and B is true.
  2. Find either \(\mathbf { P Q }\) or \(\mathbf { Q P }\) in terms of \(k\).

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]}}