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Solution to system of linear equations in range of system matrix 
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#1
Sep609, 05:15 PM

P: 11

1. The problem statement, all variables and given/known data
See image. a) and b) have been solved. The problem is c) 2. Relevant equations 3. The attempt at a solution I really have no idea where to begin. For the three systems given there are solutions x in range(A) for system 1 and 2 but not for 3. Therefore I have been trying to spot some obvious difference between system matrix A of system 2 and 3 but I cannot think of any clearly different property that could be linked to b. Any hint just to get me started would be much appreciated. 


#2
Sep609, 09:59 PM

P: 39

Hint: Ask yourself whether [itex] A^T y = 0 [/tex] has solutions such that [itex] y^T b \neq 0[/itex].
Try it yourself first. Then if you think you know what is going on, look at the wikipedia entry under Fredholm alternative. 


#3
Sep709, 12:09 AM

P: 11

Much appreciated!



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