Determine all values of the constant k for which the vectors (1,0, 1, k), (-1,0,k, 1), and (2,0,1, 3) are linearly independent in R3.

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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21:44 C
2. Determine all values of the constant k for which the
vectors (1,0, 1, k), (-1,0, k, 1), and (2,0, 1, 3) are
linearly independent in R³.
3. Use the Wronskian to determine whether the
functions are linearly independent or linearly
dependent over the interval (-o; ∞)
fi(x) = e2x; f2(x) = e3*; f3(x) = e¯*
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Transcribed Image Text:21:44 C 2. Determine all values of the constant k for which the vectors (1,0, 1, k), (-1,0, k, 1), and (2,0, 1, 3) are linearly independent in R³. 3. Use the Wronskian to determine whether the functions are linearly independent or linearly dependent over the interval (-o; ∞) fi(x) = e2x; f2(x) = e3*; f3(x) = e¯* Add a caption... > Status (Custom)
20:25 C
1. Let V = Poo be the vector space of polynomials. Is
the set {1+x + x²;1 – x; 1 – x³ } linearly
independent? Prove your claim.
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Transcribed Image Text:20:25 C 1. Let V = Poo be the vector space of polynomials. Is the set {1+x + x²;1 – x; 1 – x³ } linearly independent? Prove your claim. Add a caption... > Status (Custom)
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