MHB How Are the Vectors $z_1$, $z_2$, and $z_3$ Created in the Span?

[karush]

ok I am trying to solve some other problems following this example but can[t see how the $z_1,z_2,z_3$ are created
I know it is pulled for REFF matrix

 

[Evgeny.Makarov]

$z_1$ is one solution to the system of equations. It is obtained by putting $x_3=1$, $x_5=x_6=0$ and computing dependent variables $x_1$, $x_2$ and $x_4$.