 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-iv/1/d/iv/solution

Since

V \neq = 0

, iii gives

a^{'} \cdot (b^{'} \times c^{'}) = 1/ V \neq = 0

. The criterion in a therefore proves that $a^{'}, b^{'}, c^{'}$ are non-coplanar. In particular they form a basis of

R^{3}

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