Chapter 8.1, Problem 15E

To determine

To write the augmented matrix for the system of linear equations $\{\begin{array}{c}2x+y=7\\ x+y=2\end{array}$ .

Answer to Problem 15E

  $\left[\begin{array}{cccc}2& 1& ⋮& 7\\ 1& 1& ⋮& 2\end{array}\right]$

Explanation of Solution

Given information:

The system of linear equations given is $\{\begin{array}{c}2x+y=7\\ x+y=2\end{array}$ .

Calculations:

First, Re-write the linear equations by aligning the variables.

Here variables are already aligned $\{\begin{array}{c}2x+y=7\\ x+y=2\end{array}$ .

In augmented matrix, the coefficients and constant terms are used as the matrix entries. Row 1 contains the coefficients and constant terms of the first equation and Row 2 will contain the coefficients and constant terms of the second equation. Include zeros for the coefficients of the missing variables but since here, no variable is missing, therefore,

  $\left[\begin{array}{cccc}2& 1& ⋮& 7\\ 1& 1& ⋮& 2\end{array}\right]$

This is the augmented matrix for the given system of linear equations.