Q. 17 - 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.

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

Step-by-Step Solution

Answer

The resultant matrix is 

$\left[\begin{array}{ccc}1& -3|& -2\\ 0& 1|& 9\end{array}\right]$

Step 1. Given Information

The given matrix and operation is 

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

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,

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

Apply the given row operation on the given augmented matrix and then simplify

$$\begin{gathered} \left[\begin{array}{ccc}1& -3|& -2\\ 2& -5|& 5\end{array}\right]\to \left[\begin{array}{ccc}1& -3 |& -2\\ -2\left(1\right)+2& -2(-3)+(-5)|& -2(-2)+5\end{array}\right] \\ \to \left[\begin{array}{ccc}1& -3|& -2\\ 0& 1 |& 9\end{array}\right] \end{gathered}$$