To get a specific entry in an augmented matrix to be zero, determine the appropriate row operation that will eliminate the current value. This typically involves multiplying one row by a constant and adding it to the target row. For instance, if the first entry in row $2$ is $4$ and the first entry in row $1$ is $1$, multiplying row $1$ by $-4$ and adding it to row $2$ (documented as $-4R_1 + R_2$) will result in a $0$ in the target position. Performing the arithmetic across all corresponding entries in the rows completes the operation and produces an equivalent matrix.