 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/digital-systems-linear-algebra-and-introduction-to-formal-proof/5/a/solution

Take

V = R^{2}

h (x, y) = (x, 0)

. Then

R (h) = span {(1, 0)}, N (h) = span {(0, 1)} .

These two vector subspaces have zero intersection and together span

R^{2}

, so $V = R (h) \oplus N (h)$ as a direct sum of vector spaces.

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