Can someone help me that how can we contract a spanning set to form a basis?

Question

anonymous · Answer

There are 2 ways.

Grow.

Start with a vector of the spanning set, and add one by 1 the others vectors, only if the new vectors are not linear combinations of already existing vectors. Repeat so for all vectors, inserting 1 by one. The resulting set is a basis.

Shrink.

Start with all the spanning set vectors, and drop out 1 by one, if it is linear combination of the others vectors that are in the spanning set. Repeat so for each vector. The remaining vectors will form a basis.

anonymous · Answer

Thank You !

anonymous · Answer

Does anyone know the best way to study Linear Algebra ? I am finding the proofs a bit tough. Anyone has any suggestions?