Question

Write the augmented matrix of the following system of equations.

system

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

Short answer

Thus, the augmented matrix of system of equation is $\left[\begin{array}{cccc}1& 1& -1& 1\\ 1& 0& 2& -3\\ 0& 2& -1& 3\\ & & & \end{array}\right]$

Step-by-step solution

Step 1. Given information

A set of linear equations is given as-

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

Step 2. Concept used

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.

Step 3. Calculation

Here, we have to complete the augmented matrix.

So, we complete the augmented matrix by picking the coefficients of $x,y,z$and constant term in order as follows:

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