 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/digital-systems-linear-algebra-introduction-to-formal-proof/6/a/solution

An elementary matrix acts on rows by multiplication on the left. Apply the desired elementary row operation to the identity matrix to construct it. In the order requested, the three elementary matrices and their inverse matrices are

E_{1} = 200010001, E_{1}^{- 1} = 1/2 00 010001;

E_{2} = 10 - 2 010001, E_{2}^{- 1} = 102010001;

E_{3} = 100001010, E_{3}^{- 1} = E_{3} .

The inverse operations halve row 1, add twice row 1 to row 3, and interchange rows 2 and 3 again, respectively.

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