Determine whether the given vector functions are linearly dependent or linearly independent on the interval (-...

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Determine whether the given vector functions are linearly dependent or linearly independent on the interval (- 00,00). t-1 sin t 5t 5t sin t 5t Select the correct choice below, and fill in the answer box to complete your choice. O A. The vector functions are linearly dependent since there exists constants c1, c2, and c3, not all 0, such that c, t-1 sin t 5t +C2 5t + C3 = 0 for all t sin t 5t in I. In particular, c, = , C2 = C3 O B. The vector functions are linearly dependent since there is only one combination of c. c2, and cz that satisfy the equation t-1 sin t 5t = 0 for all t in I. In particular c, = 5t C3 = %3D 5t sin t OC. The vector functions are linearly independent since there is only one combination of c1, c2, and c3 that satisfy the equation t-1 sin t 5t = 0 for all t in I. In particular, c, = 5t C3 5t sin t OD. t-1 sin t + C, sin t The vector functions are linearly independent since there exists constants c1. C2, and c3, not all 0, such that c = 0 for all 5t t in I. In particular, C = C2 C3 = Determine whether the given vector functions are linearly dependent or linearly independent on the interval (- 00,00). t-1 sin t 5t 5t sin t 5t Select the correct choice below, and fill in the answer box to complete your choice. O A. The vector functions are linearly dependent since there exists constants c1, c2, and c3, not all 0, such that c, t-1 sin t 5t +C2 5t + C3 = 0 for all t sin t 5t in I. In particular, c, = , C2 = C3 O B. The vector functions are linearly dependent since there is only one combination of c. c2, and cz that satisfy the equation t-1 sin t 5t = 0 for all t in I. In particular c, = 5t C3 = %3D 5t sin t OC. The vector functions are linearly independent since there is only one combination of c1, c2, and c3 that satisfy the equation t-1 sin t 5t = 0 for all t in I. In particular, c, = 5t C3 5t sin t OD. t-1 sin t + C, sin t The vector functions are linearly independent since there exists constants c1. C2, and c3, not all 0, such that c = 0 for all 5t t in I. In particular, C = C2 C3 =