Q. 4.79 - Intermediate Algebra

Question

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

Step-by-Step Solution

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 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 $2$.

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