Determine whether the given vector functions are linearly dependent or linearly independent on the interval (- o,0). HE 2t 2t sin t sin t 2t sin t Selett ne Comeci Choice below, and im he answer box to cOMpiete your CTOICE. O A. The vector functions are linearly dependent since there exists constants c,, C,, and c3, not all 0, such that 2t 2t + C3 + C2 2t sin t = 0 for all t in I. In particular, c, C1 sin t C2 = + C3 = sin t O B. The vector functions are linearly independent since there exists constants c,, C2, and ca, not all 0, such that sin t |= 0 for all t in I. In particular, c, sin t 2t 2t C1 sin t + C2 + C3 C2 = C3 = 2t OC. The vector functions are linearly dependent since there is only one combination of c1, c2, and c3 that satisfy the

Determine whether the given vector functions are linearly dependent or linearly independent on the interval (- o,0). HE 2t 2t sin t sin t 2t sin t Selett ne Comeci Choice below, and im he answer box to cOMpiete your CTOICE. O A. The vector functions are linearly dependent since there exists constants c,, C,, and c3, not all 0, such that 2t 2t + C3 + C2 2t sin t = 0 for all t in I. In particular, c, C1 sin t C2 = + C3 = sin t O B. The vector functions are linearly independent since there exists constants c,, C2, and ca, not all 0, such that sin t |= 0 for all t in I. In particular, c, sin t 2t 2t C1 sin t + C2 + C3 C2 = C3 = 2t OC. The vector functions are linearly dependent since there is only one combination of c1, c2, and c3 that satisfy the

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

Determine whether the given vector functions are linearly dependent or linearly independent on the interval (- o,00).
2t
2t
sin t
sin t
2t
sin t
Selett ne Comeci Choice below, and iim he answer box lo COMpiele your thIOICE.
O A. The vector functions are linearly dependent since there exists constants c,, C,, and c3, not all 0, such that
2t
+C2
sin t
2t
+ C3
sin t
2t
= 0 for all t in I. In particular, c, =
C2 =
C3 =
sin t
O B. The vector functions are linearly independent since there exists constants c,, C2, and ca, not all 0, such that
C1
sin t
2t
C2
2t
sin t
+ C3
2t
sin t
|= 0 for all t in I. In particular, c1
C2 =
C3
OC. The vector functions are linearly dependent since there is only one combination of c4, C2, and c3 that satisfy the
sin t
= 0 for all t in I. In particular c, =|
sin t
2t
2t
equation c
sin t
+ C3
C3 =
-C2
C2 =
2t
O D. The vector functions are linearly independent since there is only one combination of c1, C2, and cz that satisfy the
2t
+C2
sin t
2t
+ C3
sin t
2t
equation c
= 0 for all t in I. In particular, c, =
C2 =, C3 =
sin t

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