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Determine whether the functions y1 and y2 are linearly dependent on the interval (0,1)

Determine whether the functions y1 and y2 are linearly dependent on the interval (0,1)

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 functions y1 and y2 are linearly dependent on the interval (0,1)
y1 = 2 cos t-1, Y2 = 12 cos 2t %3D
Transcribed Image Text:y1 = 2 cos t-1, Y2 = 12 cos 2t %3D
Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = ( D2 on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) O B. Since y, = ( Dy2 on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.) O C. Since y, is not a constant multiple of y2 on (0,1), the functions are linearly dependent on (0,1). O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0,1).
Transcribed Image Text:Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = ( D2 on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) O B. Since y, = ( Dy2 on (0,1), the functions are linearly dependent on (0,1). (Simplify your answer.) O C. Since y, is not a constant multiple of y2 on (0,1), the functions are linearly dependent on (0,1). O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0,1).
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