OCR MEI FP1 2008 January — Question 1 5 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2008
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear transformations
TypeArea scale factor from determinant
DifficultyModerate -0.8 This is a straightforward Further Maths question requiring basic matrix multiplication and direct application of the determinant-area relationship. Part (i) is routine computation, and part (ii) simply requires finding |BA| and multiplying by 3, with no conceptual challenges beyond recall of the standard result.
Spec4.03b Matrix operations: addition, multiplication, scalar4.03i Determinant: area scale factor and orientation

1 You are given that matrix \(\mathbf { A } = \left( \begin{array} { r r } 2 & - 1 \\ 0 & 3 \end{array} \right)\) and matrix \(\mathbf { B } = \left( \begin{array} { r r } 3 & 1 \\ - 2 & 4 \end{array} \right)\).
  1. Find BA.
  2. A plane shape of area 3 square units is transformed using matrix \(\mathbf { A }\). The image is transformed using matrix B. What is the area of the resulting shape?

1 You are given that matrix $\mathbf { A } = \left( \begin{array} { r r } 2 & - 1 \\ 0 & 3 \end{array} \right)$ and matrix $\mathbf { B } = \left( \begin{array} { r r } 3 & 1 \\ - 2 & 4 \end{array} \right)$.\\
(i) Find BA.\\
(ii) A plane shape of area 3 square units is transformed using matrix $\mathbf { A }$. The image is transformed using matrix B. What is the area of the resulting shape?

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