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Sep 15, 2013 at 0:05 comment added Turbo I changed the question. May be this is more correct.
Sep 15, 2013 at 0:05 history edited Turbo CC BY-SA 3.0
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Sep 15, 2013 at 0:04 comment added Turbo May be should I ask it this way? ".... is it possible to find regions such that if the system has one solution it is unique".
Sep 14, 2013 at 23:55 comment added Turbo @GerryMyerson I am just seeing if it is possible to design some parameters. It seems to come down to the case whether I can force such a linear system to have an unique solution. I have control over $a_i$s and I know that my system always has one solution. However the design forces me to have only one solution and I looking for the possibility that if I constrain my ranges for $x_i$s, may be I can force it to have always one solution. Even for $k=2$, I know that I will have a solution.
Sep 14, 2013 at 23:03 comment added Gerry Myerson What happens in the case $k=2$? And what do you do if there is no solution with $x_i\lt a_i$?
Sep 14, 2013 at 19:09 history edited Turbo CC BY-SA 3.0
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Sep 14, 2013 at 19:04 history edited Turbo CC BY-SA 3.0
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Sep 14, 2013 at 18:53 history edited Turbo CC BY-SA 3.0
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Sep 14, 2013 at 18:44 history edited Turbo CC BY-SA 3.0
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Sep 14, 2013 at 18:39 history asked Turbo CC BY-SA 3.0