OCR Further Pure Core 2 2024 June — Question 3

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2024
SessionJune
TopicMatrices

3 Matrices \(\mathbf { A }\) and \(\mathbf { B }\) are given by \(\mathbf { A } = \left( \begin{array} { r r } 4 & - 3
- 2 & 2 \end{array} \right)\) and \(\mathbf { B } = \left( \begin{array} { r r } 3 & - 5
0 & 1 \end{array} \right)\).
  1. Find 2A - 4B.
  2. Write down the matrix \(\mathbf { C }\) such that \(\mathbf { A C } = 2 \mathbf { A }\).
  3. Find the value of \(\operatorname { det } \mathbf { A }\).
  4. In this question you must show detailed reasoning. Use \(\mathbf { A } ^ { - 1 }\) to solve the equations \(4 \mathrm { x } - 3 \mathrm { y } = 7\) and \(- 2 \mathrm { x } + 2 \mathrm { y } = 9\).