 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/digital-systems-linear-algebra-introduction-to-formal-proof-resit/6/b/ii/solution

E_{n}

{u}

. For

n \geq 2

E_{0} = {v : j \sum v_{j} = 0} = span {e_{1} - e_{n}, \dots, e_{n - 1} - e_{n}} .

The displayed vectors are linearly independent by their first

n - 1

coordinates, and every vector with zero coordinate sum has exactly that expansion. At

n = 1

this list is empty and the kernel is

{0}

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