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## Homework Statement

given the matrix

https://scontent.fhlz2-1.fna.fbcdn....=7f5d6372c263996c6a11969b072d1349&oe=5BF8F2B7

https://scontent.fhlz2-1.fna.fbcdn....=7f5d6372c263996c6a11969b072d1349&oe=5BF8F2B7

in RREF

we see solution to this system is x

_{1}+x

_{2}+x

_{3}= 0

in the textbook it says which solutions are spanned by the vectors f

_{1}= (−1, 1, 0)

^{T}and f

_{2}= (−1, 0, 1)

^{T}

## Homework Equations

## The Attempt at a Solution

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I don't really understand how this is the case? Is the only way to see this to find all possible solutions to this system and then make sure each solution is linearly independent ? Or set x

_{1}= 1 (since x

_{1}is the only leading variable) and then clearly the system is only satisfied when (x

_{1}, x

_{2}, x

_{3}) = (1, -1, 0) or (1, 0, -1), but then why in the text book would they set the pivot to -1 and not just 1 ?

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