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Past exam of the mathematics course of the University of Oxford

2017

Prelims

Mathematics I

{c}

The elimination in <2/c/i> determines $x_3$ uniquely exactly when $\lambda\ne5$. The other two coordinates are then also fixed. Explicitly,
$$
\boxed{\lambda\ne5:\quad
\mathbf x=\begin{pmatrix}
1-2(\mu-2)/(\lambda-5)\\
2-5(\mu-2)/(\lambda-5)\\
(\mu-2)/(\lambda-5)
\end{pmatrix}.}
$$
For $\lambda=5$, the reduced equation is either inconsistent or leaves $x_3$ free, so a unique solution is impossible.

Solution

Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics I / 2 / c / ii / Solution

Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics I / 2 / c / ii / Solution

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Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics I / 2 / c / ii / Solution

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