OCR MEI FP1 2010 January — Question 2 7 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMatrices
TypeMatrix multiplication
DifficultyModerate -0.8 This is a straightforward Further Maths question testing basic matrix operations: checking dimensions for compatibility, performing simple matrix multiplications and addition, and composing transformations. While it's FP1 content, it requires only mechanical application of standard procedures with no problem-solving or conceptual insight, making it easier than average even on an absolute scale.
Spec4.03a Matrix language: terminology and notation4.03b Matrix operations: addition, multiplication, scalar

2 You are given that \(\mathbf { A } = \left( \begin{array} { r } 4 \\ - 2 \\ 4 \end{array} \right) , \mathbf { B } = \left( \begin{array} { r r } 5 & 1 \\ 2 & - 3 \end{array} \right) , \mathbf { C } = \left( \begin{array} { l l l } 5 & 1 & 8 \end{array} \right)\) and \(\mathbf { D } = \left( \begin{array} { r r } - 2 & 0 \\ 4 & 1 \end{array} \right)\).
  1. Calculate, where they exist, \(\mathbf { A B } , \mathbf { C A } , \mathbf { B } + \mathbf { D }\) and \(\mathbf { A C }\) and indicate any that do not exist.
  2. Matrices \(\mathbf { B }\) and \(\mathbf { D }\) represent transformations B and D respectively. Find the single matrix that represents transformation B followed by transformation D.

2 You are given that $\mathbf { A } = \left( \begin{array} { r } 4 \\ - 2 \\ 4 \end{array} \right) , \mathbf { B } = \left( \begin{array} { r r } 5 & 1 \\ 2 & - 3 \end{array} \right) , \mathbf { C } = \left( \begin{array} { l l l } 5 & 1 & 8 \end{array} \right)$ and $\mathbf { D } = \left( \begin{array} { r r } - 2 & 0 \\ 4 & 1 \end{array} \right)$.\\
(i) Calculate, where they exist, $\mathbf { A B } , \mathbf { C A } , \mathbf { B } + \mathbf { D }$ and $\mathbf { A C }$ and indicate any that do not exist.\\
(ii) Matrices $\mathbf { B }$ and $\mathbf { D }$ represent transformations B and D respectively. Find the single matrix that represents transformation B followed by transformation D.

\hfill \mbox{\textit{OCR MEI FP1 2010 Q2 [7]}}