Question 1 Which set of three vector-valued functions is linearly independent? None of these ° [][2][-]...
A9.4.13 Question Help Determine whether the given vector functions are linearly dependent or linearly independent on the interval (-00,00). Let x = Select the correct choice below, and fill in the answer box to complete your choice. 5t O A. The vector functions are linearly dependent since there exists at least one point tin (-00,00) where det[xy(t) x2(t)] is not 0. In fact, det[x4(t) x2(t)] - OB. The vector functions are linearly independent since there exists at least one point...
determine whether the set vector is M2,2 is linearly independent or linearly dependent - 1-[ : 13-1:-)-E -6 17]
Question 5 Is the set of functions linearly dependent or linearly independent? f(x) = 7, g(x) = 5x +1, h(x) = 3x2 - 4x + 5 Linearly dependent Linearly independent Have no clue... Question 6 Given a solution to the DE below, find a second solution by using reduction of order. r’y' – 3xy + 5y = 0; y1 = r* cos(In x) y2 = xsin(In x) y2 = x2 sin Y2 = 2 * sin(In) . . y2 =...
(7) Show that the functions e', cos(t), ta are linearly independent in the vector space Cº. What is the dimension of the subspace of Cºo which is spanned by these three functions?
t2 2t 2) Consider the vector functions x1) (t)- (a) In what intervals they are linearly independent? (b) Is it true that they are fundamental solution set of a linear 2 x 2-system 1c) and t interval I-(-5,16)? If yes, find the related linear system (c) The same question from (b) but on the interval 1 = (1,00). t2 2t 2) Consider the vector functions x1) (t)- (a) In what intervals they are linearly independent? (b) Is it true that...
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
Question 2 Determine if the following functions are linearly independent or dependent: Question 2 Determine if the following functions are linearly independent or dependent:
Are the following vector set {q1,q2,q3} linearly independent? ---- -}
Determine whether the following set of functions on R is linearly independent: {1 + x, x + x 2 , x2 + x 3 , x3 + 1} .
1. (16 points) Determine whether the given set of functions is linearly dependent or linearly independent on the indicated interval. Justify your answers. (a) (8 points) S(x) = x + 2cos?x, S2(x) = 3 sin’x, S(x) = x + 2 on (0,0). (b) (8 points) (x) = and f(x) = differential equation " + 1" 4x are solutions of the linear homogeneous O on () 12