Use the function to find the image of v and the preimage of w. T(V₁ V₂) (V₁ + V₂ V₁ V₂), V(7,-4), w =(5, 11) ■ (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)
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- (5.4) (6) Find the projection of the vector v onto the subspace S. S = span 0 1 1 , 1 1 0 v = 3 4 2 projs v = ??7. Find an initial point P of a nonzero vector m = P& with ter-minal point O(3. 0. -5) and such that B) u is oppositely directed to v = (4, -2,-1)Suppose the random vector X = (X1, X2, X3, X4)^T moment generating function. ((X1, X2, X3, X4)^T <- T is Transpose) Mx(t1,t2,t3,t4) = (1-t2-4t1)^(-5) * (1-t3-t4)^(-4) Find the first two moments of X1, X2, X3, and X4. Are X1 and X2 independent? (X1, X2) and (X3, X4) are independent? (X1, X3) and (X2, X4) are independent?
- If Z1, Z2, Z3 are independent and identically distributed, such that Zi--Geom(0.4) for i=1,2,3. What is P(Z1+Z2+Z3=7)?The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain, in general?)Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1, 2).
- 7.4 Let F(x,y,z)=(−7xz2,9xyz,−2xy3z)F(x,y,z)=(−7xz2,9xyz,−2xy3z) be a vector field and f(x,y,z)=x3y2zf(x,y,z)=x3y2z.∇f=(∇f=( , , )).∇×F=(∇×F=( , , )).F×∇f=(F×∇f=( , , )).F⋅∇f=F⋅∇f=Let A =[ 4 -1 2 , -1 8 3 ,1 -2 5 ] b=[1 ,-2,3] and initial vector x 0=[0,0,0,0] perform two itearation of the gauss seidel methodRecall that we say that a random variable X is in the vector space L^2 if it has finite second moment, EX^2 In this problem we will understand a bit better the geometry of the vector space L^2(1) Show that ||X||_2 = √EX^2 is a norm