 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2018/2/b/solution

c = M d, c_{i} = M_{ij} d_{j} .

Then the displayed tensor contraction is

(a_{i} c_{i}) b_{k} - (a_{i} b_{i}) c_{k} = (a \cdot c) b_{k} - (a \cdot b) c_{k}

, precisely the

k

a \times (b \times c)

M

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