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5. Prove that the functions ex, sin(x), cos(x) = F(R,R) are linearly independent. 6. Let S = {v1, v2, ..., Un} be a linearly independent subset of a vector space V and let v Є V be a vector not in span(S). Prove that X = {v1,..., Un, v} is linearly independent.

5. Prove that the functions ex, sin(x), cos(x) = F(R,R) are linearly independent. 6. Let S = {v1, v2, ..., Un} be a linearly independent subset of a vector space V and let v Є V be a vector not in span(S). Prove that X = {v1,..., Un, v} is linearly independent.

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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5. Prove that the functions ex, sin(x), cos(x) = F(R,R) are linearly independent.
Transcribed Image Text:5. Prove that the functions ex, sin(x), cos(x) = F(R,R) are linearly independent.
6. Let S = {v1, v2, ..., Un} be a linearly independent subset of a vector space V and let v Є V be a vector not in span(S). Prove that X = {v1,..., Un, v} is linearly independent.
Transcribed Image Text:6. Let S = {v1, v2, ..., Un} be a linearly independent subset of a vector space V and let v Є V be a vector not in span(S). Prove that X = {v1,..., Un, v} is linearly independent.
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