. Guided Proof Let be a spanning set for the

Chapter 4, Problem 4.323

(choose chapter or problem)

. Guided Proof Let be a spanning set for the finitedimensional vector space Prove that there exists asubset of that forms a basis forGetting Started: is a spanning set, but it may not be abasis because it may be linearly dependent. You need toremove extra vectors so that a subset is a spanning setand is also linearly independent.(i) If is a linearly independent set, then you aredone. If not, remove some vector from that is alinear combination of the other vectors in Callthis set(ii) If is a linearly independent set, then you are done.If not, then continue to remove dependent vectorsuntil you produce a linearly independent subset(iii) Conclude that this subset is the minimal spanningset S.