(1 point) Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(t)...
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,...
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
(1 point) Are the functions f, g, and h given below linearly independent? f(x) = 621 + cos(9x), g(x) = 621 – cos(9x), h(x) = cos(9x). If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. (e24 + cos(9x)) + (e21 – cos(9x)) + (cos(9.x)) = 0.
(1 point) Are the functions f, g, and h given below linearly independent? f(x) = €3x – cos(4x), g(x) = 23x + cos(4x), h(x) = cos(4x). If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. (e3x – cos(4x)) + (83x + cos(4x)) + (cos(4x)) = 0.
Show that the functions of t: 1t, 1 + f,e'are linearly independent. Hint: if a function is identically zero, so are its derivatives 2.
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 =...
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...
Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If the Wronskian W(8,9)(to) #0 for some to E I, then f and g are linearly independent for all te I. • If f(t) and g(t) are linearly dependent on I, then W (8,9)(t) = 0 for allt € 1. Note: This does NOT say that "If W(8,9)(x) = 0, then f(x) and g(2) are linearly dependent. Problem 2 Determine if the following functions are...
9. (12 pts) Determine whether the following functions are linearly independent. [ 3e-t [0] 2e (a) xi(t) = -2 , x2(t) = |e3t, x3(t) = 5e L-e- [O] Lel (b) f(x) = 2x2020, g(x) = 2,2020 cos2, h(x) = 2.2020 sinº r.
a) they are linearly independent b)they are linearly dependent c)neither linearly dependent nor linearly independent d)functions cannot be determined in real space x e) none of them (10,00 Puanlar) 2 14,(x) = [1 - Cos(2x)]. uz(x) = Sin?(x) fonksiyonlarının lincer bağımlı yada lineer bağımsız olup olmadıklarını inceleyiniz? a uneer olarak bagimsizdirlar by Lineer olarak bagimlidirlar. Ne lineer bagimline de lineer bagimsizdirlar d Fonksiyonlar, x-reel uzayında belirlenemezdirler c) Hiçbiri Once 2/ Soncalo > Kaput Swim