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Question
Under what conditions on a, b, c will vector v=[a,b,c] belong to
span {[1,-1,3],[3,-2,7],[1,1,-1]}

I don't understand how to find the span

Answer
Based on the previous Q&A, we can determine if the vectors listed are linearly independent, and thus span 3-D and contain v, if the determinant of the matrix of the vectors is zero. The calculation reveals that det ≠ 0. So we can write, for instance,

c1a + c2b = c

where c1 and c2 are constants i.e., c is a linear combination of a and b. This condition can also be written equivalently as c3b + c4c + a or c5a + c6c = b.

Randy

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randy patton

Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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Also an Expert in Oceanography

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