Chapter 8.1, Problem 20E

To determine

To write the augmented matrix for the system of linear equations $\{\begin{array}{c}9x+y-3z=21\\ -15y+13z=-8\end{array}$ .

Answer to Problem 20E

  $\left[\begin{array}{ccccc}9& 1& -3& ⋮& 21\\ 0& -15& 13& ⋮& -8\end{array}\right]$

Explanation of Solution

Given information:

The system of linear equations given is $\{\begin{array}{c}9x+y-3z=21\\ -15y+13z=-8\end{array}$ .

Calculations:

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

Here variables are already aligned $\{\begin{array}{c}9x+y-3z=21\dots (1)\\ -15y+13z=-8\dots (2)\end{array}$ .

In augmented matrix, the coefficients and constant terms are used as the matrix entries. Row 1, and Row 2 contains the coefficients and constant terms of the (1) and (2) equation respectively. Also,include zeros for the coefficients of the missing variables, like in equation (1) variable x is missing, so zero will be written as its coefficient.

  $\left[\begin{array}{ccccc}9& 1& -3& ⋮& 21\\ 0& -15& 13& ⋮& -8\end{array}\right]$

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