This is not a homework question. But a question on how to understand what my textbook does.(adsbygoogle = window.adsbygoogle || []).push({});

It is about choosing the free variables.

Let's say I have the system of equations:

x1-2x2+3x3+2x4+x5 =10

x3 +2x5=-3

x4 -4x5=7

Then my book says that we choose x2 and x5 to be free variables, since they are not leading. And we set

x2=t and x4=s and solve the system.

But why do we have to choose x2 and x5 just because they are not leading? I mean, Can't I say x2=t and x5=s instead of x4?

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# Linear algebra, free variables

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