Edexcel F1 2018 June — Question 4 7 marks

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2018
SessionJune
Marks7
PaperDownload PDF ↗
TopicMatrices
TypeSolving matrix equations for unknown matrix
DifficultyStandard +0.3 This is a straightforward Further Maths matrix question requiring standard techniques: finding a 2×2 inverse using the determinant formula, then solving for X by post-multiplying both sides by A^(-1). The algebra simplifies nicely with the parameters p and q canceling out. While it's Further Maths content (making it slightly above average), it's a routine textbook exercise with no conceptual challenges or novel insights required.
Spec4.03n Inverse 2x2 matrix4.03o Inverse 3x3 matrix

4. $$\mathbf { A } = \left( \begin{array} { c c } 2 p & 3 q \\ 3 p & 5 q \end{array} \right)$$ where \(p\) and \(q\) are non-zero real constants.
  1. Find \(\mathbf { A } ^ { - 1 }\) in terms of \(p\) and \(q\). Given \(\mathbf { X A } = \mathbf { B }\), where $$\mathbf { B } = \left( \begin{array} { c c } p & q \\ 6 p & 11 q \\ 5 p & 8 q \end{array} \right)$$
  2. find the matrix \(\mathbf { X }\), giving your answer in its simplest form.

4.

$$\mathbf { A } = \left( \begin{array} { c c } 
2 p & 3 q \\
3 p & 5 q
\end{array} \right)$$

where $p$ and $q$ are non-zero real constants.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathbf { A } ^ { - 1 }$ in terms of $p$ and $q$.

Given $\mathbf { X A } = \mathbf { B }$, where

$$\mathbf { B } = \left( \begin{array} { c c } 
p & q \\
6 p & 11 q \\
5 p & 8 q
\end{array} \right)$$
\item find the matrix $\mathbf { X }$, giving your answer in its simplest form.
\end{enumerate}

\hfill \mbox{\textit{Edexcel F1 2018 Q4 [7]}}