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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
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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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
Transcribed Image Text: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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