Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). y, = e' 3t Y2 = e - 2t ..... Select the correct choice below and, if necessary, fill in the answer box within your choice. А. Since y, = ( y2 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). D. Since y, is not a constant multiple of y2 on (0,1), the functions are linearly independent on (0,1).
Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). y, = e' 3t Y2 = e - 2t ..... Select the correct choice below and, if necessary, fill in the answer box within your choice. А. Since y, = ( y2 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). D. Since y, is not a constant multiple of y2 on (0,1), the functions are linearly independent on (0,1).
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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Transcribed Image Text:Determine whether the functions y, and y2 are linearly dependent on the interval (0,1).
3t
Y, = e ", y, = e -2t
.....
Select the correct choice below and, if necessary, fill in the answer box within
your
choice.
A. Since y, = Dy2 on (0,1), the functions are linearly independent on (0,1).
(Simplify your answer.)
В.
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).
D. Since y, is not a constant multiple of y2 on (0,1), the functions are linearly independent on (0,1).
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