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Vector Space : Linear Dependence and Null Space

If there are n vectors v1, v2, v3...vn in E^m, which spans a subspace of dimension k<=n. If k<n, how many different linear dependencies will there be among v1, v2, v3...vn? Can we determine the theorem about the null space and range of a linear transformation about this? (See attachment for full question)


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Linear dependence of vectors and null space are investigated.