Problem 5. The functions f(x) = 2x and g(x) = |x| can be considered elements of the vector space C[a, b] for any interval [a, b] CR. Show that f(x) and g(x) are linearly independent in C[-1, 1] while being linearly dependent in C[0, 1].
Problem 5. The functions f(x) = 2x and g(x) = |x| can be considered elements of the vector space C[a, b] for any interval [a, b] CR. Show that f(x) and g(x) are linearly independent in C[-1, 1] while being linearly dependent in C[0, 1].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![Problem 5. The functions f(x) = 2x and g(x) = |x| can be considered elements of the
vector space C[a, b] for any interval [a, b] CR. Show that f(x) and g(x) are linearly independent
in C[-1, 1] while being linearly dependent in C[0, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d370c3-9e4b-442d-9a89-d591c5ced338%2F4e94c5f5-1103-47b4-97cb-aa0837916c90%2Fww02bzj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 5. The functions f(x) = 2x and g(x) = |x| can be considered elements of the
vector space C[a, b] for any interval [a, b] CR. Show that f(x) and g(x) are linearly independent
in C[-1, 1] while being linearly dependent in C[0, 1].
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