Solution to system of linear equations in range of system matrix

kalleC

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.

Attached Thumbnails

 

loveequation

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.

kalleC

Much appreciated!