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: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, givingMultiplication 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.