| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2021 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Matrices |
| Type | Singular matrix conditions |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question testing standard matrix theory. Part (a) requires setting the determinant equal to zero and solving a quadratic equation. Part (b) applies the standard 2×2 matrix inversion formula. Both parts are routine applications of well-practiced techniques with no problem-solving insight required, making it easier than average even for Further Maths. |
| Spec | 4.03h Determinant 2x2: calculation4.03l Singular/non-singular matrices4.03n Inverse 2x2 matrix |
3. The matrix $\mathbf { M }$ is defined by
$$\mathbf { M } = \left( \begin{array} { c c }
k + 5 & - 2 \\
- 3 & k
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Determine the values of $k$ for which $\mathbf { M }$ is singular.
Given that $\mathbf { M }$ is non-singular,
\item find $\mathbf { M } ^ { - 1 }$ in terms of $k$.\\
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\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2021 Q3 [4]}}