Chapter 11.2, Problem 17AYU

In Problems 19-26, write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.

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

To determine

To find: The system of equations corresponding to the given augmented matrix and perform the indicated row operation on this augmented matrix:

$\left(\begin{array}{cc}1& -3\\ 2& -5\end{array}|\begin{array}{c}-2\\ 5\end{array}\right);R_2=-2r_1+r_2$

Answer to Problem 17AYU

Solution:

$x-3y=-2$

$2x-5y=5$

$\left(\begin{array}{cc}1& -3\\ 0& 1\end{array}|\begin{array}{c}-2\\ 9\end{array}\right)$

Explanation of Solution

Given:

$\left(\begin{array}{cc}1& -3\\ 2& -5\end{array}|\begin{array}{c}-2\\ 5\end{array}\right);R_2=-2r_1+r_2$

Calculation:

The system of equations corresponding to the given augmented matrix is:

$x-3y=-2$

$2x-5y=5$

The augmented matrix after the row operation: $R_2=-2r_1+r_2$ is:

$\left(\begin{array}{cc}1& -3\\ -2+2& -2\left(-3\right)-5\end{array}|\begin{array}{c}-2\\ -2\left(-2\right)+5\end{array}\right)=\left(\begin{array}{cc}1& -3\\ 0& 6-5\end{array}|\begin{array}{c}-2\\ 4+5\end{array}\right)$ or $\left(\begin{array}{cc}1& -3\\ 0& 1\end{array}|\begin{array}{c}-2\\ 9\end{array}\right)$.