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Solution to system of linear equations in range of system matrix

by kalleC
Tags: equations, linear, matrix, range, solution
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Sep6-09, 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.
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Sep6-09, 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.
Sep7-09, 12:09 AM
P: 11
Much appreciated!

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