# Write the augmented matrix for the system of linear equations 2y-z=7 x+2y+z=17 2x-3y+2z=-1

Question
Forms of linear equations
Write the augmented matrix for the system of linear equations
2y-z=7
x+2y+z=17
2x-3y+2z=-1

2020-11-10
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
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,
$$[(0,2,-1),(1,2,1),(2,-3,2)][(7),(17),(-1)]$$

### Relevant Questions

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A small grocer finds that the monthly sales y (in $) can be approximated as a function of the amount spent advertising on the radio $$x_1$$ (in$) and the amount spent advertising in the newspaper $$x_2$$ (in $) according to $$y=ax_1+bx_2+c$$ The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months. $$\begin{array}{|c|c|c|}\hline \text { Advertising, } x_{1} & \text { Advertising, } x_{2} &\text{sales, y} \\ \hline 2400 & { 800} & { 36,000} \\ \hline 2000 & { 500} & { 30,000} \\ \hline 3000 & { 1000} & { 44,000} \\ \hline\end{array}$$ a) Use the data to write a system of linear equations to solve for a, b, and c. b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c) Write the model $$y=ax_1+bx_2+c$$ d) Predict the monthly sales if the grocer spends$250 advertising on the radio and \$500 advertising in the newspaper for a given month.