| Exam Board | OCR |
|---|---|
| Module | FP1 AS (Further Pure 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Topic | Matrices |
| Type | Matrix inverse calculation |
| Difficulty | Moderate -0.8 This is a routine Further Maths FP1 question testing standard matrix operations: calculating a 3×3 determinant (with one parameter), identifying singularity condition, and finding the inverse using the adjugate method. All steps are algorithmic with no problem-solving required. While 3×3 matrices are more involved than 2×2, this remains a textbook exercise below average difficulty even for Further Maths students. |
| Spec | 4.03j Determinant 3x3: calculation4.03l Singular/non-singular matrices4.03o Inverse 3x3 matrix |
2 The matrix $\mathbf { A }$ is given by $\mathbf { A } = \left( \begin{array} { r r c } 2 & 1 & 2 \\ 1 & - 1 & 1 \\ 2 & 2 & a \end{array} \right)$.
\begin{enumerate}[label=(\alph*)]
\item Show that $\operatorname { det } \mathbf { A } = 6 - 3 a$.
\item State the value of $a$ for which $\mathbf { A }$ is singular.
\item Given that $\mathbf { A }$ is non-singular find $\mathbf { A } ^ { - 1 }$ in terms of $a$.
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 AS 2021 Q2 [7]}}