| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | 3x3 Matrices |
| Type | Matrix equation solving (AB = C) |
| Difficulty | Standard +0.3 This is a straightforward Further Maths matrix question requiring matrix multiplication and recognition that AB = μI means B = μA^(-1). The calculation is routine but involves 3×3 matrices which adds some computational work. The conceptual insight (recognizing the relationship to find B^(-1)) is standard for FP1 level, making this slightly easier than average overall. |
| Spec | 4.03c Matrix multiplication: properties (associative, not commutative)4.03o Inverse 3x3 matrix |
| Answer | Marks |
|---|---|
| Multiply \(\mathbf{AB}\) and compare with \(\mu\mathbf{I}\) | M1 |
| \(\lambda = 3\), \(\mu = 1\) | A1 A1 A1 |
| Answer | Marks |
|---|---|
| Since \(\mathbf{AB} = \mathbf{I}\), \(\mathbf{B}^{-1} = \mathbf{A}\) | M1 |
| \(\mathbf{B}^{-1} = \begin{pmatrix}3 & 6 & -4 \\ 2 & 5 & -1 \\ -1 & 4 & 3\end{pmatrix}\) | A1 |
## Question 3:
**(i)**
Multiply $\mathbf{AB}$ and compare with $\mu\mathbf{I}$ | M1 |
$\lambda = 3$, $\mu = 1$ | A1 A1 A1 |
**(ii)**
Since $\mathbf{AB} = \mathbf{I}$, $\mathbf{B}^{-1} = \mathbf{A}$ | M1 |
$\mathbf{B}^{-1} = \begin{pmatrix}3 & 6 & -4 \\ 2 & 5 & -1 \\ -1 & 4 & 3\end{pmatrix}$ | A1 |
---3 You are given that $\mathbf { A } = \left( \begin{array} { c c c } \lambda & 6 & - 4 \\ 2 & 5 & - 1 \\ - 1 & 4 & 3 \end{array} \right) , \mathbf { B } = \left( \begin{array} { c c c } - 19 & 34 & - 14 \\ 5 & - 5 & 5 \\ - 13 & 18 & - 3 \end{array} \right)$ and $\mathbf { A B } = \mu \mathbf { I }$, where $\mathbf { I }$ is the $3 \times 3$ identity\\
matrix.\\
(i) Find the values of $\lambda$ and $\mu$.\\
(ii) Hence find $\mathbf { B } ^ { - 1 }$.
\hfill \mbox{\textit{OCR MEI FP1 2016 Q3 [6]}}