(1 point) Let u = (-2,-3) and v = (-1,6). Then u+v=< >, u-v=< -3v=< u.V=...
(1 point) Let u= (3, 2) and v = (1,5). Then u +v=< 7 U-v=< -30 =< u. V = and || 0 ||
Qi. Let x be a real number and u, v be the vectors u =< x,-V3x >, v =< -x,-3 > a) Find the value(s) of x if u.v 6 b) Let x v3, find the angle between the vectors u and v
PROB5 Let U and V be independent r.v's such that the p.d.f of U is fu(u) = { 2 OSU< 27, otherwise. and the p.d.f'of2 is Seu, v>0, fv (v otherwise. Let X = V2V cos U and Y = 2V sin U. Show that X and Y are independent standard normal variables N(0,1).
Let u =
Problem 4 Suppose U and V follow uniform [0, 1] independently. (1) Let X = min( UV). Let F(x) = P(X<2). Calculate F(2) and f(c). (2) Let Y = max(U,V). Let F(y) = P(Y = y). Calculate F(y) and f(y). (3) Let Z=U + V. Let F(z) = P(Z < z). Calculate F(2) and f(z).
1. Let u - (1,1,2), v = (1,2,1), and w (2,1,1) in R. and consider • the parallelogram B = {s(3v) + t-w) 0 <s,t<1, s,te R} spanned/formed by the vectors (3v) and (-w), and • the parallelepiped P = {ru + s(3v) + (-w) 0 <T,,t<1, r, s, t€ R} [10] spanned formed by vectors u. (3v). and (-w) We take the parallelogram B as a base of P. (a) Does the ordered vector triple (v xw, 3v, -w),...
(1 point) Let (u, v) = (7u+ 3v, 5u + 8v). Use the Jacobian to determine the area of (R) for: (a)R = [0, 4] × [0,9) (b)R = [2, 19] x [6, 10] (a)Area (D(R)) = (b)Area (“(R)) = 1
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
3) Let u a) Treating u, v', and w' as vectors, are the inner products u.v', v'.u, and u.w' defined? If yes, compute them. If any of them is not defined, explain why not. b) Treating u, v', and ' as matrices, are the products uv', v'u, and w' defined? If yes, compute them. If any of them is not defined, explain why not.
two parts! thank you! Find u + v. u = (5, - 4) and v= (-3, -5) u u+v=< 0) (Simplify your answers.) Use the paralelogram de to find the magnitude of the resultant force for the two foroes shown in the figure. The magrouse of the room force Round on the