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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.

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.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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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¯* Add a caption... > Status (Custom)
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. Add a caption... > Status (Custom)
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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