The equals signs in the system of equations are represented with a vertical bar in the matrix.
The coefficients of the variables form the columns on the left-hand side of the bar.
The constants form the column on the right-hand side of the bar.
Below we demonstrate this in a generalized form.
a_(11)x+ a_(12)y+ a_(13)z= c_1 a_(21)x+ a_(22)y+ a_(23)z= c_2 a_(31)x+ a_(32)y+ a_(33)z= c_3
⇕
[
ccc|c
a_(11) & a_(12) & a_(13) & c_1
a_(21) & a_(22) & a_(13) & c_2
a_(31) & a_(32) & a_(13) & c_3
]
Because the variables in the given system are not in the same order, our first step will be to write each equation in the same order. It will also help us visualize the process if we leave spaces for any missing variables.
x+3y- z=2 x +2z=8 2y- z=1
Next, let's consider the coefficients and the constants. If there is ever a missing variable, we should treat it as though it has a coefficient of 0.
1x+ 3y - 1z= 2 1x+ 0y+ 2z= 8 x+ 2y - 1z= 1
Now that we have identified all of the variables and constants, we can place them in a matrix.
[
ccc|c
1 & 3 & -1 & 2
1 & 0 & 2 & 8
& 2 & -1 & 1
]
