complex gauss-jordan elimination algorithm

Question

anonymous · Answer

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anonymous · Answer

when I tried to adjust it by normal GJ algorithm i got stuck at
1 1 -1 | 0
0 0  0  | 0
0 0  0  | 0

anonymous · Answer

The answer is x(1)= -s + t x(2) = s x(3) = t

jim_thompson5910 · Answer

hmm i'm getting that too, but idk what you mean by *complex* GJ elimination

anonymous · Answer

I don't know where the t and s came from in the book's solution

jim_thompson5910 · Answer

oh i see

1     1    -1     0

means

x(1) + x(2) - x(3) = 0

So if x(3) and x(2) are your free variables, then 

x(2) = s
x(3) = t

jim_thompson5910 · Answer

Plug them into x(1) + x(2) - x(3) = 0 and solve for x(1)

x(1) + x(2) - x(3) = 0

x(1) + s - t = 0

x(1) = -s + t

anonymous · Answer

I don't understand what you mean by this 

So if x(3) and x(2) are your free variables, then x(2) = s x(3) = t

jim_thompson5910 · Answer

free variables are just variables 

so if x(2) is a free variable, then x(2) = s

This basically says "x(2) is some unknown number 's'"

jim_thompson5910 · Answer

and it's allowed to be "free" to be whatever it wants

anonymous · Answer

That makes sense. i feel like this solution is cheating. :/ But I guess I can't get an exact value so this is the only way to write it. Thanks for your help once more

jim_thompson5910 · Answer

well that's as close as we get to writing all of the possible solutions (there are infinitely many of them)

anonymous · Answer

Thats true. I didn't include it in the post but it does say to find all solutions