 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/digital-systems-linear-algebra-introduction-to-formal-proof/5/c/iv/solution

A linear map is one-to-one, or injective, when equal outputs imply equal inputs. Equivalently its kernel is

{0}

: subtracting inputs converts equality of outputs to a zero output. Here $T$ is not one-to-one, since its kernel has dimension two. Concretely,

T (- 2, - 1, 1, 0) = T (0) = 0

for distinct inputs.

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