wronskian is never zero for any t so they are linearly independent so they form fundamental set of solutions to Y'=AY
2. (5pts Determine whether the following set of vectors is a fundamental set of solutions of...
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of the O.D.E.? C) State the general solution for this O.D.E. a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of...
(1 point) Which of the following vectors forms a fundamental set of solutions to the system of differential equations X') X? 0 6 0 21 6t 0 14t 0 0 6t. 6t
7. If y, and y2 are a fundamental set of solutions of t2y"-2/ + (3 + t)y = 0 and if won,n)(2) = 4, find the value of W(vi.v2)(3).
The vectors 3 X3 =|-6|+t|4 X2 х, =|-2|+ t 12 are solutions of a system X' = AX Determine whether the vectors form a fundamental set of solutions.
2. [5pts] Given that y 1, e are solutions to the homogeneous version of the nonhomogeneous DE below, verify that they form a fundamental set of solutions. Then, use variation of parameters to find the general solution y(t)
1. Consider a set of vectors S = {X1, X2, X3 } in which X1 = (1,0,0), X2 = (a, 1, -a), X3 = (1, 2, 3a +1) Determine the value (or values) of a for which the set Sabove is linearly independent (LI). 2. Consider a set of vectors T = {y1, y2.ya} in which yı = (1,2,0), y2 = (1, m,5), and y3 = (0,4, n) Determine a condition on m and n such that the set T...
Consider the differential equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p and q are continuous on some open interval I. Choose some point t0 in I. Let y1 be the solution of equation (1) that also satisfies the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the solution of equation (1) that satisfies the initial conditions y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set...
3. (30pt) Suppose that E(Y) = 1, E(Y2) = 2, E(Y3) = 3, V(Y1) = 6, V(Y2) = 7,V (Y3) = 8, Cov(Yı, Y2) = 0, Cov(Yı, Y3) = -4 and 10 1 2 3 Cov(Y2, Y3) = 5. Also define a = 20 and A = 4 5 6 30/ ( 7 8 9 (a) (10pt) Find the expected value and variance covariance matrix of Y, where Y = Y2 (b) (10pt) Compute Eſa'Y) and E(AY). (c) (10pt) Compute...
linear algebra 1. Determine whether the given set, along with the specified operations of addition and scalar multiplication, is a vector space (over R). If it is not, list all of the axioms that fail to hold. a The set of all vectors in R2 of the form , with the usual vector addition and scalar multiplication b) R2 with the usual scalar multiplication but addition defined by 31+21 y1 y2 c) The set of all positive real numbers, with...
3. Use reduction of order to find the fundamental set of solutions and write the general solution, given that y1 is a solution xy" – (4x + 1)y' + (4x + 2)y = 0, Y1 = e2x