Vector and matrices are the independent or dependent

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SUMMARY

The discussion focuses on determining the linear independence of the vectors v1 = [1, -1; 0, 0], v2 = [2, -2; 1, ...], and v3 = [-5, 5; 1, 0]. The key conclusion is that these vectors are dependent, as one can be expressed as a linear combination of the others. Additionally, the span of {v1, v2, v3} does not include the vector W = [4, 4; 4, 4], which can be demonstrated through the properties of linear combinations and the definition of span.

PREREQUISITES
  • Understanding of linear independence and dependence in vector spaces
  • Familiarity with matrix representation of vectors
  • Knowledge of linear combinations and spans
  • Basic proficiency in solving systems of equations
NEXT STEPS
  • Study the concept of linear independence in depth using "Linear Algebra Done Right" by Sheldon Axler
  • Practice solving linear systems with "Gaussian elimination" techniques
  • Explore the "Span" and its implications in vector spaces
  • Learn about "Basis" and "Dimension" in linear algebra
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Students of linear algebra, educators teaching vector spaces, and anyone seeking to understand the concepts of linear independence and span in mathematical contexts.

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Vector and matrices...are the independent or dependent

Homework Statement



Determine whether the vectors v1=[1,-1;0,0],v2=[2,-2;1,... and v3=[-5,5;1,0] are independent or dependent. Find the span {v1,v2,v3} and give a description. Explain why W = [4,4;4,4,] is not in the span {v1,v2,v3}.

Homework Equations


I have tried solving this problem in matrix form...I'm not sure if this is the correct way



The Attempt at a Solution


Please help
 
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Use the definition of linear independence to show the vectors are independent, or show that they're dependent by writing one as a linear combination of the others. You need to show some work here before people will help.
 

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