Question

Write the augmented matrix of the given system of equations.

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

Short 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-by-step solution

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,

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