Linear independence and decompostion

by MotoPayton
Tags: decompostion, independence, linear
MotoPayton is offline
Oct4-11, 06:10 PM
P: 96
Explain why the method of decomposition when applied to the solution set of a homogeneous linear system always yields a linearly independent set of vectors whose span is the set of solutions....

Can someone explain this it seems reasonable but I can't seem to prove it to myself
Phys.Org News Partner Science news on
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)
MotoPayton is offline
Oct5-11, 01:24 PM
P: 96
Maybe dependent spans do not exist because if that were to be the case the dependence would work itself out in the rref as a definite solution removing the dependence. So only independent spans form....

Bacle is offline
Oct6-11, 12:59 AM
P: 662
Maybe if you explain to us what the method is, we can help you better, and, in doing the explaining, you may understand things better yourself.

Register to reply

Related Discussions
Linear algebra: subspaces, linear independence, dimension Calculus & Beyond Homework 3
Linear Algebra - Linear Independence/Dependence Calculus & Beyond Homework 3
Linear Algebra: Linear Independence and writing Matrices as linear combinations Calculus & Beyond Homework 7
2 Linear Algebra Proofs about Linear Independence Calculus & Beyond Homework 2
Linear Algebra: Linear Transformation and Linear Independence Calculus & Beyond Homework 8