Q. 4.80 - Intermediate Algebra

Question

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

Step-by-Step Solution

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 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 $2$.

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