 Solution

ID: 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/c/i/solution

First subtract row one from row two, using

E_{1}

; then subtract four times the updated row two from row three, using

E_{2}

E_{1} = 1 - 1 0 010001, E_{2} = 100 01 - 4 001 .

The updated second row is

(0, 1, 2)

and the final third row is

(0, 0, - 4)

. Hence

E_{2} E_{1} A = U

and

L = E_{1}^{- 1} E_{2}^{- 1}

. The resulting LU decomposition is

L = 110014001, U = 100110 12 - 4, A = LU .

Reversing the order when undoing the elementary operations is essential.

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