Solution to system of linear equations in range of system matrix


by kalleC
Tags: equations, linear, matrix, range, solution
kalleC
kalleC is offline
#1
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.
Attached Thumbnails
problem.jpg  
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
loveequation
loveequation is offline
#2
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.
kalleC
kalleC is offline
#3
Sep7-09, 12:09 AM
P: 11
Much appreciated!


Register to reply

Related Discussions
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