 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/digital-systems-linear-algebra-and-introduction-to-formal-proof/4/a/solution

The

m

columns of

L

form a basis of

ker A^{⊤}

m

A^{⊤} : R^{n} \to R^{n}

gives

rank A^{⊤} = n - m

. A matrix and its transpose have equal matrix rank, hence

rank A = n - m .

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