Question

Perform the needed row operation that will get the first entry in row $2$to be zero in the augmented matrix:$\left[\begin{array}{rrr}1& -1& 2\\ 3& -6& 2\end{array}\right]$

Short answer

Multiply row $1$by $-3$and then add it to row $2$.

$\left[\begin{array}{rrr}1& -1& 2\\ 0& -3& -4\end{array}\right]$

Step-by-step solution

Step 1. Given Information.

Given augmented matrix is$\left[\begin{array}{rrr}1& -1& 2\\ 3& -6& 2\end{array}\right]$

Step 2. Making first entry in row 2 to zero.

To make the $3$to $0$, we could multiply row $1$by $-3$and then add it to row $2$.

role="math" localid="1644470898545" $\left[\begin{array}{rrr}1& -1& 2\\ 3& -6& 2\end{array}\right]\stackrel{-3R_1+R_2}{\to }\left[\begin{array}{rrr}1& -1& 2\\ 0& -3& -4\end{array}\right]$