Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Digital systems, linear algebra, introduction to formal proof / 5 / a

Table of contents
- i a
  - Solution i
- ii a
  - Solution ii

i

Solution

The required elementary matrix is

E = 001010100, E^{- 1} = E .

Left multiplication exchanges the two rows. Applying the same exchange twice restores every row, so

E^{2} = I_{3}

.

ii

Solution

The elementary row operation and its reverse are

F = 100 01 - 3 001, F^{- 1} = 100013001 .

Thus

F A

replaces row three by row three minus three times row two. The inverse adds those three copies back.

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