 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/digital-systems-linear-algebra-introduction-to-formal-proof/4/a/i/solution

D_{ij} = \sum_{k = 1}^{N} B_{ik} C_{kj}

. A potentially nonzero term requires

k = i

because

B

k = j

because

C

i \neq = j

these requirements cannot both hold. Thus every summand is zero and $D_{ij} = 0$ whenever $i \neq = j$ .

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