OCR MEI
Further Pure Core AS
2024
June
— Question 5
Exam Board
OCR MEI
Module
Further Pure Core AS (Further Pure Core AS)
Year
2024
Session
June
Topic
Roots of polynomials
5
Find the volume scale factor of the transformation with associated matrix \(\left( \begin{array} { r r r } 1 & 2 & 0 0 & 3 & - 1 - 1 & 0 & 2 \end{array} \right)\).
The transformations S and T of the plane have associated \(2 \times 2\) matrices \(\mathbf { P }\) and \(\mathbf { Q }\) respectively.
Write down an expression for the associated matrix of the combined transformation S followed by T.
The determinant of \(\mathbf { P }\) is 3 and \(\mathbf { Q } = \left( \begin{array} { r r } k & 3 - 1 & 2 \end{array} \right)\), where \(k\) is a constant.
Given that this combined transformation preserves both orientation and area, determine the value of \(k\).