Q. 16 - Precalculus Enhanced with Graphing Utilities

Question

Write the augmented matrix of the given system of equations. 

$$\begin{gathered} x-y+2z-w=5 \\ x+3y-4z+2w=2 \\ 3x-y-5z-w=-1 \end{gathered}$$

Step-by-Step Solution

Answer

The augmented matrix of system of equation is 

$\left[\begin{array}{ccccc}1& -1& 2& -1|& 5\\ 1& 3& -4& 2|& 2\\ 3& -1& -5& -1|& -1\end{array}\right]$

Step 1. Given Information

The given equations are 

$$\begin{gathered} x-y+2z-w=5 \\ x+3y-4z+2w=2 \\ 3x-y-5z-w=-1 \end{gathered}$$

Step 2. Explanation

For writing an augmented matrix, the variables of each equation in the system of equations must be on the left side of equal sign and constraints on the right side. A variable that does not appear in the equation has coefficient zero. Thus, the augmented matrix of system of equation is as follows, 

$\left[\begin{array}{ccccc}1& -1& 2& -1|& 5\\ 1& 3& -4& 2|& 2\\ 3& -1& -5& -1|& -1\end{array}\right]$