| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795 (Pre-U Further Mathematics) |
| Session | Specimen |
| Marks | 10 |
| Topic | 3x3 Matrices |
| Type | Find inverse then solve system |
| Difficulty | Standard +0.3 This is a standard Further Maths linear algebra question requiring matrix inversion (using cofactors/adjugate method) and solving systems of equations. Part (b) adds mild conceptual depth by asking about consistency conditions and geometric interpretation, but the techniques are routine for Further Maths students. Slightly above average difficulty due to the computational work and the consistency analysis, but well within expected syllabus material. |
| Spec | 4.03o Inverse 3x3 matrix4.03r Solve simultaneous equations: using inverse matrix4.03s Consistent/inconsistent: systems of equations |
\begin{enumerate}[label=(\alph*)]
\item Find the inverse of the matrix $\begin{pmatrix} 1 & 3 & 4 \\ 2 & 5 & -1 \\ 3 & 8 & 2 \end{pmatrix}$, and hence solve the set of equations
\begin{align}
x + 3y + 4z &= -5, \\
2x + 5y - z &= 10, \\
3x + 8y + 2z &= 8.
\end{align} [5]
\item Find the value of $k$ for which the set of equations
\begin{align}
x + 3y + 4z &= -5, \\
2x + 5y - z &= 15, \\
3x + 8y + 3z &= k,
\end{align}
is consistent. Find the solution in this case and interpret it geometrically. [5]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9795 Q10 [10]}}