Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof / 3 / c

Use Gaussian elimination without row exchanges. First apply $R_2\leftarrow R_2-3R_1$ and $R_3\leftarrow R_3-2R_1$; then apply $R_3\leftarrow R_3-R_2$:The elimination multipliers are $m_{21}=3$, $m_{31}=2$ and $m_{32}=1$. Put them below the diagonal of a unit lower triangular matrix:To see why these multipliers reconstruct the rows, row 2 of $LU$ is three times row 1 of $U$ plus row 2 of $U$, giving $(3,8,14)$. Row 3 of $LU$ is twice row 1 plus row 2 plus row 3 of $U$, giving $(2,6,13)$. This directly verifies the LU factorization.