 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/digital-systems-linear-algebra-introduction-to-formal-proof-resit/5/a/solution

An elementary matrix acts on rows by left multiplication. In the stated order, the three matrices are

E_{s} = 1000010000300001, E_{a} = 1000 010 - 3 00100001, E_{p} = 0001010000101000 .

The first scales row 3, the second adds

- 3

times row 2 to row 4, and the third swaps rows 1 and 4. Right multiplication would instead perform column operations.

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