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skysurani
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f1(x)= (sqrtx) + 5,
f2(x)= (sqrtx) + 5x
f3(x)= x-1
i don't know how to start
f2(x)= (sqrtx) + 5x
f3(x)= x-1
i don't know how to start
Prove whether or not the following are linearly independent
- Thread starter skysurani
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- Independent Linearly
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SUMMARY
The discussion focuses on determining the linear independence of the functions f1(x) = (sqrt(x)) + 5, f2(x) = (sqrt(x)) + 5x, and f3(x) = x - 1. Participants emphasize the importance of applying definitions related to linear independence, specifically the need to identify the set of functions being analyzed. The conclusion drawn is that a systematic approach using definitions is essential for proving linear independence.
PREREQUISITES- Understanding of linear independence in vector spaces
- Familiarity with function notation and algebraic manipulation
- Knowledge of the definition of a linear combination
- Basic calculus concepts, particularly involving square root functions
- Study the definition of linear independence in the context of vector spaces
- Learn how to determine linear combinations of functions
- Explore examples of proving linear independence using specific functions
- Review calculus techniques for analyzing functions, including limits and continuity
Mathematics students, educators, and anyone involved in linear algebra or functional analysis who seeks to deepen their understanding of linear independence among functions.
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