Which of the Following Sets of Vectors Are Linearly Independent

The linear structure of sets of vectors lets us say much more about one-to-one and onto functions than one can say about functions on general sets. Then we can show that a linear transformation is one-to-one if and only if 0 V is the only vector that is sent to 0 W.

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Any two bases of a vector space V have.

. For example we always know that a linear function sends 0 V to 0 W. By looking at just one very special vector we can. The importance of bases lies in the fact that they are simultaneously minimal generating sets and maximal independent sets.

More precisely if S is a linearly independent set and T is a spanning set such that S T then there is a basis B such that S B T. A set of vectors is linearly independent if none is in the span of the others.

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