Question

Use Row Operations on a Matrix In the following exercises, perform the indicated operations on the augmented matrices.

Perform the needed row operation that will get the first entry in row 2 to be zero in the augmented matrix:

$\left[\begin{array}{rrr}1& 2& 5\\ -3& -4& -1\end{array}\right]$

Short answer

The required matrix is$\left[\begin{array}{lll}1& 2& 5\\ 0& 2& 14\end{array}\right]$.

Step-by-step solution

Step 1. Given Information

A matrix is given as $\left[\begin{array}{rrr}1& 2& 5\\ -3& -4& -1\end{array}\right]$

Step 2. Explanation 

A matrix is given as $\left[\begin{array}{rrr}1& 2& 5\\ -3& -4& -1\end{array}\right]$

Apply given operation as-

$$\begin{gathered} \left[\begin{array}{rrr}1& 2& 5\\ -3& -4& -1\end{array}\right]\stackrel{3R+R_2}{⟶}\left[\begin{array}{ccc}1& 2& 5\\ (3\times 1)-3& (3\times 2)-4& (3\times 5)-1\end{array}\right] \\ \stackrel{3A_1+R_2}{⟶}\left[\begin{array}{lll}1& 2& 5\\ 0& 2& 14\end{array}\right] \end{gathered}$$