Q 208 - Intermediate Algebra

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:

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

Step-by-Step Solution

Answer

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

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-

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