Find a Basis for R^4 Subspace Spanning S

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SUMMARY

The discussion focuses on finding a basis for the subspace of R^4 spanned by the set S = {(6, -3, 6, 340), (3, -2, 3, 19), (8, 3, -9, 6), (-2, 0, 6, -5)}. Participants emphasize the importance of determining the linear independence of these vectors. If the vectors are linearly independent, they form a basis for the 4-dimensional subspace. If not, the process involves eliminating dependent vectors and reassessing the remaining set.

PREREQUISITES
  • Understanding of linear independence in vector spaces
  • Familiarity with R^4 and its properties
  • Knowledge of basis and dimension concepts in linear algebra
  • Proficiency in performing row reduction or Gaussian elimination
NEXT STEPS
  • Study methods for determining linear independence of vectors in R^4
  • Learn about Gaussian elimination techniques for vector sets
  • Explore the concept of basis and dimension in vector spaces
  • Investigate applications of subspaces in higher-dimensional linear algebra
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Students and professionals in mathematics, particularly those studying linear algebra, as well as educators teaching vector space concepts.

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Find a basis for the subspace of R^4 spanned by, S={(6,-3,6,340, (3,-2,3,19), (8,3,-9,6), (-2,0,6,-5)

Not too sure where to start.
 
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Start by figuring out if they're linearly independent. If they are, the subspace is 4-dimensional, and those vectors are a basis. If they're not, you can eliminate one and repeat the procedure with the ones you have left.
 

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