 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof-resit/5/a/iii/solution

True. A square matrix with matrix rank

n

is invertible, and its transpose has the same rank. Applying the rank-nullity theorem to both

A

and

A^{T}

gives nullity zero in each case, so both kernels are

{0}

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