Question

Perform the needed row operation that will get the first entry in row $2$to be zero in the augmented matrix:role="math" localid="1644471362101" $\left[\begin{array}{rrr}1& -1& 3\\ -2& -3& 2\end{array}\right]$

Short answer

Multiply row $1$by $2$and add it to row $2$.

$\left[\begin{array}{rrr}1& -1& 3\\ 0& -5& 8\end{array}\right]$

Step-by-step solution

Step 1. Given Information.

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

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

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

$\left[\begin{array}{rrr}1& -1& 3\\ -2& -3& 2\end{array}\right]\stackrel{2R_1+R_2}{\to }\left[\begin{array}{rrr}1& -1& 3\\ 0& -5& 8\end{array}\right]$