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For this matrix:

How do I know what the free variables are? Are they $x_4$ and $x_5$ ?

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  • $\begingroup$ @Amzoti Hm? The lost column is what the systems of equations equal. Imagine a small line inbetween that column and the rest of the matrix $\endgroup$
    – user98535
    Oct 5, 2013 at 21:24
  • $\begingroup$ The first nonzero entry of each row flags the dependent variables. The rest will be the free variables. $\endgroup$
    – Maesumi
    Oct 5, 2013 at 21:24
  • $\begingroup$ @Maesumi So it would be $x_2$ and $x_4$ $\endgroup$
    – user98535
    Oct 5, 2013 at 21:25

1 Answer 1

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We have, from the bottom up:

  • $x_5 = 1$
  • $x_3 = 2 + x_4$
  • $x_1 = 8 + 3 x_4 + 4 x_2$

So, our free variables are $x_2$ and $x_4$.

You are 'free' to choose any values you want for those, with the observation that two of the solution are dependent on those values.

Try some examples to see what is going on.

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  • $\begingroup$ Ah I understand! Thank you $\endgroup$
    – user98535
    Oct 5, 2013 at 21:26

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