# Solution to system of linear equations in range of system matrix

by kalleC
Tags: equations, linear, matrix, range, solution
 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. Attached Thumbnails
 P: 39 Hint: Ask yourself whether $A^T y = 0 [/tex] has solutions such that [itex] y^T b \neq 0$. Try it yourself first. Then if you think you know what is going on, look at the wikipedia entry under Fredholm alternative.
 P: 11 Much appreciated!

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