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Past exam of the mathematics course of the University of Oxford

2015

Prelims

Mathematics I

{c}

The relevant <inner products> are
$$
\langle1,x\rangle=\frac{-1+0+1}{3}=0,\qquad
\langle1,1\rangle=1,\qquad\langle x,x\rangle=\frac23.
$$
Hence $1$ and $x$ are <orthogonal vectors>. Dividing by their <norms> gives the <orthonormal basis>
$$
\boxed{f=1,\qquad g=\sqrt{\frac32}\,x}
$$
of their <linear span> $U$.

Solution

Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics I / 4 / b / i / Solution

Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics I / 4 / b / i / Solution

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Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics I / 4 / b / i / Solution

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