Answer
The system of equations is:
$\left\{\begin{array}{llll}
x & -3y & =-2\\
2x & -5y & =5\\
\end{array}\right.$
Performing the indicated operations yield:
$\left[\begin{array}{cc|c} {1}&{-3}&{-2}\\ {0}&{1}&{9}\end{array}\right]$
Work Step by Step
The standard form of a linear equation can be expressed as:
$a_{i1}x_{1}+a_{i2}x_{2}+..........+a_{in}x_{n}=b_{i}$
where, the index $i$ indicates that it is the i-th equation of a system of equations.
In order to write the augmented matrix $[A|B]$ of a system of equations in standard form, we must follow some important points: 1. To express a system in matrix form, we must extract the coefficients of the variables and constants.
2. Draw a vertical line to separate the coefficient entries from the constants (essentially replacing the equal signs).
3. The entries of the coefficient matrix $A=[a_{ij}]$ must be placed to the left of the lline.
4. The constants of the $B=[b_{i}]$ must be placed to the right of the line.
The system of equations can be expressed as follows:
$\left\{\begin{array}{llll}
x & -3y & =-2\\
2x & -5y & =5\\
\end{array}\right.$
We can write the system as an augmented matrix $[A|B]$ as follows:
$[A|B]=\left[\begin{array}{rr|r} {1}&{-3}&{-2}\\ {2}&{-5}&{5}\end{array}\right]$
We perform the row operation as: $ R_{2}=-2r_{1}+r_{2}$
$=\left[\begin{array}{cc|c} {1} &{-3} &{-2}\\ {-2+2}&{6+(-5)}&{4+5}\end{array}\right]$
$=\left[\begin{array}{cc|c} {1}&{-3}&{-2}\\ {0}&{1}&{9}\end{array}\right]$
