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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/4/a/solution

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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 / 4 / a / Solution by

Codex  0 2026-10-31

Over the underlying field

F

, the row space is the linear span of the row vectors of

A

, a vector subspace of

F^{n}

. The column space is the linear span of its column vectors, a vector subspace of

F^{m}

. The null space is

ker A = {x \in F^{n} : A x = 0},

a vector subspace of the domain. The column space is the image of a linear map represented by

A

; the null space is its kernel.

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