Solution to system of linear equations in range of system matrix

[kalleC]

Homework Statement

See image. a) and b) have been solved. The problem is c)

Homework Equations

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.

 

[loveequation]

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

 

[kalleC]

Much appreciated!