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

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SUMMARY

The vectors $z_1$, $z_2$, and $z_3$ are derived from the REFF matrix in a system of equations. Specifically, $z_1$ is calculated by setting $x_3=1$ and $x_5=x_6=0$, which allows for the computation of the dependent variables $x_1$, $x_2$, and $x_4$. This method illustrates how specific variable assignments lead to unique solutions within the span of the vector space defined by the REFF matrix.

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karush
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Screenshot 2021-02-02 at 10.30.47 AM.png

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
 
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$z_1$ 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 $x_4$.
 

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