Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Y1 =1-2 sin?t, y2 = 4 cos 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = (Dy2 on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) O B. Since y, = (Dv2 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 y2 on (0,1), the functions are linearly independent on (0,1).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 33E
icon
Related questions
Question
Determine whether the functions y, and y2 are linearly dependent on the interval (0,1).
Y1 =1-2 sin?t, y2 = 4 cos 2t
Select the correct choice below and, if necessary, fill in the answer box within your choice.
O A. Since y, = (Dy2 on (0,1), the functions are linearly independent on (0,1).
(Simplify your answer.)
O B. Since y, = (Dv2 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 y2 on (0,1), the functions are linearly independent on (0,1).
Transcribed Image Text:Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Y1 =1-2 sin?t, y2 = 4 cos 2t Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Since y, = (Dy2 on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) O B. Since y, = (Dv2 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 y2 on (0,1), the functions are linearly independent on (0,1).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Chain Rule
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning