 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/c/solution

For

v \in R (h^{m + k})

, choose

u

with

v = h^{m + k} u = h^{m} (h^{k} u)

. Thus

v \in R (h^{m})

, proving

R (h^{m + k}) \subseteq R (h^{m}) .

h^{0} = id_{V}

includes

m = 0

and

k = 0

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