Question

The Augmented Matrix Write the augmented matrix for the system of linear equations.

$\left\{\begin{array}{l}3x+y-z=2\\ 2x-y=1\\ x-z=3\end{array}\right\}$.

Short answer

The augmented matrix for the system of linear equations$\left\{\begin{array}{l}3x+y-z=2\\ 2x-y=1\\ x-z=3\end{array}\right\}$ is$\left[\begin{array}{cccc}3& 1& -1& 2\\ 2& -1& 0& 1\\ 1& 0& -1& 3\end{array}\right]$

Step-by-step solution

Step 1. Given information.

The Given Matrix$\left\{\begin{array}{l}3x+y-z=2\\ 2x-y=1\\ x-z=3\end{array}\right\}$

Step 2. write the augmented matrix for the given system of linear equations in three variables.

The matrix that represents the system of linear equations is referred to as an augmented matrix of the system, it contains the same information as the system but in a simpler form as only the coefficients and constants that appear in the equations are used.

The augmented matrix for the given system of linear equations is;

$\left[\begin{array}{cccc}3& 1& -1& 2\\ 2& -1& 0& 1\\ 1& 0& -1& 3\end{array}\right]$

$\begin{array}{l}{\text{R}}_3\to {\text{R}}_3-2{\text{R}}_2\\ A=\left[\begin{array}{cccc}1& -3& 2& -1\\ 0& 1& 1& -1\\ 0-2\left(0\right)& 2-2\left(1\right)& -1-2\left(1\right)& 1-2(-1)\end{array}\right]\end{array}$

$A=\left[\begin{array}{cccc}1& -3& 2& -1\\ 0& 1& 1& -1\\ 0& 0& -3& 3\end{array}\right]$