Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 5 / a / i / Solution

Left multiplication by an elementary matrix adds a multiple of row one to its designated target row. The first-column entries below the pivot are $1,2,-1$, so $a=-1$, $b=-2$, $c=1$. The corresponding row operations are $R_2\leftarrow R_2-R_1$, $R_3\leftarrow R_3-2R_1$, and $R_4\leftarrow R_4+R_1$. Since none changes row one, their sequential application gives the required three eliminated first-column entries and the displayed remaining entries.