help 6. (10 pts) a) Use the definition of linear dependence to show that following set...
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 =...
3 Question 25 Given a set of DE solutions: y1(x) = e* cos x and y2(x) = e sinx, a) Find the value of the Wronskian W[ v1.y2). b) Determine if the solutions Y1, Y2 are linearly independent. a)W=e b) Linearly Independent a) W=-ex b) Linearly Independent O a) W = 1 b) Linearly Independent a) W=eX b) Linearly Dependent O a) W=0 b) Linearly Dependent None of them
You are told that a certain second order, linear, constant
coefficient, homogeneous ode has the solutions
y1(x) = e^γx cos ωx, and y2(x) = e^γx sin ωx,
where γ and ω are real-valued parameters and −∞ < x <
∞.
4. You are told that a certain second order, linear, constant coefficient, homogeneous ODE has the solutions where γ and w are real-valued parameters and-oo < x < oo. (a) Compute the Wronskian for this set of solutions. (b) Using...
Ch3.2- Existence Uniqueness Wronskian: Problem 3 Previous Problem Problem List Next Problem (1 point) Use the Wronskian to determine whether the functions yı = sin(62) and y2 = cos(4.c) are linearly independent. Wronskian = det These functions are linearly independent because the Wronskian is nonzero for Choose value(s) of 2.
5. The equation axy is known as the Airy equation in honor of G. B. Airy a British astronomer who studied it in 1838 as a simple model to explain diffraction of light. Here are the plots of two solutions named as Ai(x), B(x) dx2 Aix) Bi(x) 0.00 0.25 -13 These solutions do not have a closed form (like cos(x)) Instead, they have a representation in series (2.3)(5 6)(8.9) (3k - 1)3k) 3k+1 Bi(x)x+ 4)67)(9-10)..(3k)(3k+ 1)) Either from the graphs...
Use the definition of linear independence to determine whether
the columns of the following matrix form a linearly independent or
dependent set.
2 -1 4 A= 1 3 2 0 1 1
Let Coo denote the set of smooth functions, ie, functions f : R → R whose nth derivative exists, for all n. Recall that this is a vector space, where "vectors" of Coo are function:s like f(t) = sin(t) or f(t) = te, or polynomials like f(t)-t2-2, or constant functions like f(t) = 5, and more The set of smooth functions f (t) which satisfy the differential equation f"(t) +2f (t) -0 for all t, is the same as the...
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...
2. (3+4+4+4 pts) In this problem, we discuss a method of solving SOL equations known as Reduction of Order. Given an equation y" +p(a)y' +9(2)y = 0, and assuming yi is a solution, Reduction of Order asks: does there exist a second, linearly-independent solution y2 of the form y2 = u(x)41 for some function u(x)? See Section 3.2, Exercise 36 for reference). We'll now use this to solve the following problem. (a) Consider the SOL differential equation sin(x)y" — 2...
linear algebra- Linear independence
Problems 1. Show that the following sets of vectors in R" are linearly dependent: U = (-1,2,4) and V = (5.-10,--20) in R. (b) U = (3,-1), V =(4,5) and W = (-4,7) in R2. 2. Are the following sets of vectors in R3 linearly independent or linearly dependent? Show work. (-3,0,4), (5,-1, 2) and (1, 1,3) (b) (-2,0,1), (3, 2,5), (6,-1,1) and (7,0,-2)