 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/6/c/iii/solution

No. The nonzero vector

v = (2, - 9, - 3, 21)^{⊤}

is in the kernel of the linear map, so

T (v) = T (0) = 0

although

v \neq = 0

. A linear map is injective exactly when its kernel consists only of zero.

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