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 / d

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- Solution d

Solution

The columnwise null space conditions say

A^{⊤} L = 0

and

A R = 0

. Therefore

A^{⊤} B = A^{⊤} L R^{⊤} = 0, A B^{⊤} = A (R L^{⊤}) = (A R) L^{⊤} = 0.

Both right-hand sides are the

n \times n

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