 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/ii/solution

dim V = dim ker T + dim im T

V

. Here the domain has dimension four and the image has dimension two. Thus $dim ker T = 4 - 2 = 2$ . For example, a kernel basis is

{(- 2, - 1, 1, 0), (- 1, - 2, 0, 1)}

, as follows from the reduced equations.

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