Let 2=214,4) be satisfying Žy +23-5=0. Find out a t sincz teyz 22 ay
Let ?(?)y(t) be the solution to ?′=?+?y′=t+y satisfying
?(5)=6.satisfying y(5)=6.
Use Euler's Method with time step ℎ=0.1h=0.1 to approximate
?(5.5).approximate y(5.5).
(Use decimal notation. Give your answers to four decimal
places.)
n= 0, to = 5, yo = n = 1, 11 = 5.1, yı = n = 2, 12 = 5.2, y2 = n = 3,13 = 5.3, y3 = n = 4, 14 = 5.4, y4 = n = 5, t5 = 5.5, y5 =
and 02 Let T : R2 + RP be the linear transformation satisfying 9 5 Tū1) = [ and T(v2) = [ - -5 -1 X Find the image of an arbitrary vector [ Y -([:) - 1
23 43 Problem 6. (5 pts each) True or False (Circle one and state your seaon) If t) is a solution of the DE: "+(t-t)y+Ay- 5, then so is the f Reason: rue Fa b. Let f and g be two functions, such that F(s)L0) and Go)-Li defined on (0, oo). If f(t) S 9(t) for allt 2 0, then F(o) S Glo) for als True F Reason: c. There exists a piecewise continuous and ex that LIf(0)]-3 exponential order...
idterm Exan2 Problem 1. Let satisfying t u(t) 0 and g(t) be smooth 1-periodic functions u"+gu 0 on R Show that 9(0) de go. Hint: Re-write this integral parts. in terms of functions u and u" and integrate by
idterm Exan2 Problem 1. Let satisfying t u(t) 0 and g(t) be smooth 1-periodic functions u"+gu 0 on R Show that 9(0) de go. Hint: Re-write this integral parts. in terms of functions u and u" and integrate by
3. (10 points) Let T : R3-A, T(x1, 22, 23) = (zi,-z2,23 a) Prove that T is a linear operator. b) Find the standard matrix of T.
Need Help ASAP!!!!
Subject: Linear Algebra
(a) Let A= r 7 T 5 2 4 0 1 i. Compute det A in terms of r. ii. Find all value(s) of z such that A is NOT invertible. (b) Let the characteristic polynomial of a matrix B be – 23 +22 +6%. i. Find the size of B. ii. Find all the eigenvalues of B including multiplicity. iii. Find the determinant of B.
Question: Let f(x) be a function satisfying f(0) = 0, f'(0) = 5, f'(0) = -6 and |f(3)(x) = 6 for 0 5x51. Find the Taylor polynomial of degree 2 off at x = 0 and then find lim 5x-f(x) x2 x=0+ Answer: The Taylor polynomial of degree 2 off at x = 0 is P2(x) = Near x = 0, the function f(x) is equal to P2(x) plus some remainder, that is f(x) = P2(x) + R3(x).
Algebra Let F: R- R2 be a linear transformation satisfying 0 (a) Find Fy (b) Find ker(F). In both cases you must show working to justify your answer.
Find the solution of a = y (5 – š) satisfying the initial condition y(0) = 100. (Use symbolic notation and fractions where needed.) y = Find the solution of = y (5 – }) satisfying the initial condition y(0) = 25. (Use symbolic notation and fractions where needed.) y = Find the solution of a = y (5 – š) satisfying the initial condition y(0) = -5. (Use symbolic notation and fractions where needed.) y =
3. Let La A = 1 - 2 5 -3 2 5 0 -12-2 . L (a) (8 points) It turns out that the matrix equation Ax = b is consistent only for a special type of vector b where bi, b2, and b3 satisfy a certain equation. Find this equation. (b) (8 points) The set of all vectors satisfying the equation found in part (a) equals Span {W1, w2} Find wį and w2.