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Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {e 4x, e-9x e -*) on (-∞0,00) (...) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 4x - 9x OA. The functions are linearly dependent because C₁ + C₂ e -X=0 has the solution C₁, C₂, and c3 = -1. + C3 e (Type integers or simplified fractions.) 4x e B. The functions are linearly independent because c₁ e -X=0 has no solutions for constants C₁, C₂, and c3 that are not all zero e + C₂ - 9x e + C3

Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {e 4x, e-9x e -*) on (-∞0,00) (...) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 4x - 9x OA. The functions are linearly dependent because C₁ + C₂ e -X=0 has the solution C₁, C₂, and c3 = -1. + C3 e (Type integers or simplified fractions.) 4x e B. The functions are linearly independent because c₁ e -X=0 has no solutions for constants C₁, C₂, and c3 that are not all zero e + C₂ - 9x e + C3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {e 4x, e-9x e-x) on (-00,00) (...) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 4x - 9x + C₂ e + C3 e -X=0 has the solution C₁, C₂, and c3 = -1. OA. The functions are linearly dependent because c₁ e (Type integers or simplified fractions.) 4x B. The functions are linearly independent because c₁ e e -X=0 has no solutions for constants C₁, C₂, and c3 that are not all zero. + C₂ - 9x e + C3
Transcribed Image Text:Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {e 4x, e-9x e-x) on (-00,00) (...) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 4x - 9x + C₂ e + C3 e -X=0 has the solution C₁, C₂, and c3 = -1. OA. The functions are linearly dependent because c₁ e (Type integers or simplified fractions.) 4x B. The functions are linearly independent because c₁ e e -X=0 has no solutions for constants C₁, C₂, and c3 that are not all zero. + C₂ - 9x e + C3
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