given the matrix
we see solution to this system is x1+x2+x3 = 0
in the textbook it says which solutions are spanned by the vectors f1 = (−1, 1, 0) T and f2 = (−1, 0, 1) T
The Attempt at a Solution
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 x1 = 1 (since x1 is the only leading variable) and then clearly the system is only satisfied when (x1, x2, x3) = (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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