Q. 18 - Precalculus Enhanced with Graphing Utilities

Question

Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. 

$\left[\begin{array}{ccc}1& -3|& -3\\ 2& -5|& -4\end{array}\right], R_2=-2r_1+r_2$

Step-by-Step Solution

Answer

The resultant matrix is 

$\left[\begin{array}{ccc}1& -3|& -3\\ 0& 1|& 2\end{array}\right]$

Step 1. Given Information

The given matrix and operation is 

$\left[\begin{array}{ccc}1& -3|& -3\\ 2& -5|& -4\end{array}\right], R_2=-2r_1+r_2$

Step 2. Explanation

The given matrix has two rows. So, it represents a system of two linear equations. The 2 columns to the left of vertical bar indicate that the system has two variables.

Let the variables be x and y. Then system of linear equation corresponding to the given matrix is as follows,

$$\begin{gathered} x-3y=-3---\left(1\right) \\ 2x-5y=-4---\left(2\right) \end{gathered}$$

Apply the given row operation on the given augmented matrix,

$\left[\begin{array}{ccc}1& -3|& -3\\ 2& -5|& -4\end{array}\right]\to \left[\begin{array}{ccc}1& -3|& -3\\ 0& 1|& 2\end{array}\right]$