 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof-resit/5/c/solution

For the first matrix choose its single independent column:

B_{1} = 111, C_{1} = (111) .

Their product has every column equal to

B_{1}

, and both factors have rank one.

For the second matrix, the first and third columns are independent and the second equals the first, giving

B_{2} = 120001, C_{2} = (101001) .

Multiplication reconstructs the stated matrix. The first factor has independent columns and the second has independent rows, so both have matrix rank two, as required for a rank factorization.

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