| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Singular matrix conditions |
| Difficulty | Moderate -0.8 This question tests routine matrix operations: finding when det(A)=0 for singularity (standard 2×2 determinant), computing the inverse using the formula, and recalling basic transformation matrices. All parts are direct application of standard techniques with no problem-solving or insight required, making it easier than average. |
| Spec | 4.03d Linear transformations 2D: reflection, rotation, enlargement, shear4.03l Singular/non-singular matrices4.03o Inverse 3x3 matrix |
\begin{enumerate}
\item (i) The matrix $\mathbf { A }$ is defined by
\end{enumerate}
$$\mathbf { A } = \left( \begin{array} { c c }
3 k & 4 k - 1 \\
2 & 6
\end{array} \right)$$
where $k$ is a constant.\\
(a) Determine the value of $k$ for which $\mathbf { A }$ is singular.
Given that $\mathbf { A }$ is non-singular,\\
(b) determine $\mathbf { A } ^ { - 1 }$ in terms of $k$, giving your answer in simplest form.\\
(ii) The matrix $\mathbf { B }$ is defined by
$$\mathbf { B } = \left( \begin{array} { l l }
p & 0 \\
0 & q
\end{array} \right)$$
where $p$ and $q$ are integers.\\
State the value of $p$ and the value of $q$ when $\mathbf { B }$ represents\\
(a) an enlargement about the origin with scale factor - 2\\
(b) a reflection in the $y$-axis.
\hfill \mbox{\textit{Edexcel F1 2024 Q1 [6]}}