Determine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1). y₁ = tan ²t-sec c²t₁ y₂ = 6 Select the correct choice below and, if necessary, fill in the answer box within your choice. © A. Since y₁ = (y₂ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) B. 1 Y₂ on (0,1), the functions are linearly dependent on (0,1). Since y₁ = (Simplify your answer.) C. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly independent on (0,1). D. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly dependent on (0,1).
Determine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1). y₁ = tan ²t-sec c²t₁ y₂ = 6 Select the correct choice below and, if necessary, fill in the answer box within your choice. © A. Since y₁ = (y₂ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) B. 1 Y₂ on (0,1), the functions are linearly dependent on (0,1). Since y₁ = (Simplify your answer.) C. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly independent on (0,1). D. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly dependent 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 y₁ and y₂ are linearly dependent on the interval (0,1).
y₁ = tan ²t-sec
c²t₁ y₂ = 6
Select the correct choice below and, if necessary, fill in the answer box within your choice.
© A. Since y₁ = (y₂ on (0,1), the functions are linearly independent on (0,1).
(Simplify your answer.)
B.
1
Y₂ on (0,1), the functions are linearly dependent on (0,1).
Since y₁ =
(Simplify your answer.)
C. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly independent on (0,1).
D. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly dependent on (0,1).
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