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 / 4 / c

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- Solution c

Solution

The analogous null space statement is

A x = 0 ⟺ x = R y for some y \in R^{m} .

Here the rank-nullity theorem and (a) ensure that

ker A

also has dimension

m

.

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