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
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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.

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