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Past exam of the mathematics course of the University of Oxford

2017

Prelims

Mathematics I

{c}

By <2/c/i>, a free choice of $x_3$ is possible precisely when $\lambda=5$ and $\mu=2$. Thus
$$
\boxed{\text{infinitely many solutions}\iff(\lambda,\mu)=(5,2).}
$$
The complete <solution set of a linear system> is
$$
\boxed{\mathbf x=\begin{pmatrix}1\\2\\0\end{pmatrix}
+t\begin{pmatrix}-2\\-5\\1\end{pmatrix},\quad t\in\mathbb R.}
$$
The direction <vector> spans the <kernel>, and the displayed <straight line> is the entire <solution set of a linear system>.

Solution

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

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

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

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