# Write the augmented matrix for the system of linear equations: {(2y-z=7),(x+2y+z=17),(2x-3y+2z=-1):}

Question
Equations
Write the augmented matrix for the system of linear equations:
$$\displaystyle{\left\lbrace\begin{array}{c} {2}{y}-{z}={7}\\{x}+{2}{y}+{z}={17}\\{2}{x}-{3}{y}+{2}{z}=-{1}\end{array}\right.}$$

2020-12-29
Step 1:We have to write the augmented matrix for the given system of linear equations.
An augmented matrix for the system of equations is a matrix of numbers in which each row represents the constants from one equation(both the coefficients and the constant on the other side of the equal sign.
and each column represents all the coefficients for a single variable
Given system of linear equation is,
2y−z = 7
x+2y+z=17
2x−3y+2z=−1
Step 2:
Steps to write augmented matrix,
Step 1) Write the coefficients of the x-terms as the numbers down the first column.
Step 2) Write the coefficients of the y-terms as the numbers down the second column.
Step 3) Write the coefficients of the z-terms as the numbers down the third column.
Step 4) Draw a vertical line and write the constants to the right of the line.
Therefore we get,
$$\displaystyle{\left[\begin{array}{ccc|c} {0}&{2}&-{1}&{7}\\{1}&{2}&{1}&{17}\\{2}&-{3}&{2}&-{1}\end{array}\right]}$$
This is the augmented matrix for given system of linear equations.

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