|Sep6-09, 05:15 PM||#1|
Solution to system of linear equations in range of system matrix
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.
|Sep6-09, 09:59 PM||#2|
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||#3|
|Similar Threads for: Solution to system of linear equations in range of system matrix|
|matrix equation system||Calculus & Beyond Homework||0|
|Genericity of Uniquness of a Solution to a System with Non-Linear Equations||Differential Geometry||2|
|Analytical Solution to this? -- linear system of ODES||Differential Equations||2|
|How to reduce the solution time of linear equation system?||Linear & Abstract Algebra||0|
|Patterns of Solution Sets of a System of Linear Equations||Linear & Abstract Algebra||2|