 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/iv/solution

False. Triviality of

N (A)

gives

r = n

, while triviality of

N (A^{T})

gives

r = m

because transpose preserves matrix rank. Both conditions therefore force

m = n

, contradicting the stated unequal dimensions.

 New to topics? Read the docs here!