| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | 3x3 Matrices |
| Type | Find inverse then solve system |
| Difficulty | Standard +0.3 This is a standard FP1 matrix question covering determinants, matrix inverses, and solving simultaneous equations. Part (i) requires computing a 3×3 determinant and setting it to zero (routine). Part (ii) involves finding the inverse using the adjugate method (standard algorithm). Part (iii) applies the inverse to solve equations (direct application). While it's Further Maths content, these are textbook exercises requiring methodical calculation rather than insight, making it slightly easier than an average A-level question overall. |
| Spec | 4.03j Determinant 3x3: calculation4.03o Inverse 3x3 matrix4.03r Solve simultaneous equations: using inverse matrix |
The matrix $\mathbf{B}$ is given by $\mathbf{B} = \begin{pmatrix} a & 1 & 3 \\ 2 & 1 & -1 \\ 0 & 1 & 2 \end{pmatrix}$.
\begin{enumerate}[label=(\roman*)]
\item Given that $\mathbf{B}$ is singular, show that $a = -\frac{2}{3}$. [3]
\item Given instead that $\mathbf{B}$ is non-singular, find the inverse matrix $\mathbf{B}^{-1}$. [4]
\item Hence, or otherwise, solve the equations
\begin{align}
-x + y + 3z &= 1, \\
2x + y - z &= 4, \\
y + 2z &= -1.
\end{align} [3]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 Q7 [10]}}