9. (12 pts) Determine whether the following functions are linearly independent. [ 3e-t [0] 2e (a)...
Determine whether the following set of functions on R is linearly independent: {1 + x, x + x 2 , x2 + x 3 , x3 + 1} .
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...
12. -/1 POINTS ZILLDIFFEQ8 4.1.017. Determine whether the given set of functions is linearly independent on the interval (-00,00). f(x) = 5, f(x) = cos2x, 13(x) = sinºx O linearly dependent O linearly independent Need Help? Read It Talk to a Tutor)
(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) fi(x) = x + 2cos²x, f(x) = 3sin’x, f(x) = x + 2 on (-0,co). (b) (8 points) fi(x) = e34 and 12(x) = e 4x are solutions of the linear homogeneous differential equation y" + y' - 12y = 0 on (-0,co).
Problem 2 Determine if the following functions are linearly independent or linearly dependent. If you believe that they are linearly dependent (i.e. W(5,9) (+) = 0, for all t in some interval) find a dependence relation. 1. f(t) = cost, g(t) = sint 2. f(t) = 61, g(t) = 64+2 3. f(t) = 9 cos 2t, g(t) = 2 cos? t - 2 sinat 4. f(t) = 2t>, g(t) = 14
Problem #2: Which of the following sets of functions are linearly independent on the interval (-0, c.)? [2 marks] (i) f1(x) = x, f2(x) = 4x, 13(x) = = x2 +6 (ii) f1(x) = 2e2x, 12(x) = 4e4x, f3(x) = 8e8x (iii) f1(x) = 8sinx, 12(x) = 4cos 2x, f3(x) 9 (A) (i) and (iii) only (B) (iii) only (C) none of them (D) (ii) only (E) all of them (F) (i) only (G) (i) and (ii) only (H) (ii)...
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 =...
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
(3e-4 -8t +9 Consider the vector-valued functions xi(t) = | (-2+2 + 3t) and 22(t) = 3e-4t a. Compute the Wronskian of these two vectors. Wx(t) = (67 – 33t+27)e-4t), b. On which intervals are the vectors linearly independent? If there is more than one interval, enter a comma-separated list of intervals. The vectors are linearly independent on the interval(s): (-infinity,1),(1,4.5),(4.5, infinity), help (intervals). c. Find a matrix P(t) = (Pu(t) P12(t)) so that 21 and 22 are fundamental solutions...
Determine which of the following pairs of functions are linearly independent. 1. \(f(x, y)=2 x-4 y-12, \quad g(x, y)=-3 x+6 y+18\)2. \(f(t)=17 t^{3} \quad, \quad g(t)=e^{x}\)3. \(f(\theta)=\cos (3 \theta) \quad, \quad g(\theta)=4 \cos ^{3}(\theta)-8 \cos (\theta)\)4. \(f(x)=x^{3} \quad, \quad g(x)=|x|^{3}\)5. \(f(t)=e^{\lambda t} \cos (\mu t) \quad, \quad g(t)=e^{\lambda t} \sin (\mu t) \quad, \mu \neq 0\)6. \(f(t)=4 t^{2}+28 t \quad, \quad g(t)=4 t^{2}-28 t\)7. \(f(\theta)=\cos (3 \theta) \quad, \quad g(\theta)=4 \cos ^{3}(\theta)-4 \cos (\theta)\)8. \(f(x)=e^{4 x} \quad, \quad g(x)=e^{4(x-3)}\)9. \(f(x)=x^{2} \quad,...